Out in America's promised land, in the suburbs and villages where the moneyed classes raise their families, there are increasing signs of a self-destructive, violent and perverse discontent among the children of privilege.

In the big-money North Shore suburbs of Chicago the daughter of a wealthy real estate developer drove her mother's sports car out to a park three summers ago and hanged herself from a tree. North Shore parents and their attending psychiatrists cannot forget the suicide. For Rhonda Alter, 18, was smart, beautiful and altruistic. Her father said she was "perfect." Rhonda had described the North Shore, with its circular driveways, chirping birds and white-columned homes, as a "magic land of beauty and civility."

In Postdam, N.Y., the 24-year-old son of a prominent chemistry professor came home from his wanderings last fall and entered his parents' spacious home with a knife. Glenn Goodrich, a bright but aimless young man who friends said was always dwarfed by the brilliance of his father, stabbed Frank C. Goodrich in the heart as he lay asleep and forced his mother into the master bedroom to stare at the body. "Poor dad, I was proud of my father," Goodrich told his mother, as they stood beside the bed. Then, with his father's blood, he wrote on the wallpaper above the bed: "The Horror."

Outside the Washington Hilton last March, another aimless young man from a privileged family allegedly attempted the ultimate American horror. John W. Hinckley Jr., who had failed to measure up to the success of his brother and sister, who had shrunk from the pressures of high school, whose name went unspoken when his oil-executive father talked of his successful children, stands charged with trying to kill the president of the United States.

Behind these spectacularly tragic examples of privileged kids gone wrong there is growing statistical evidence and near unanimity among mental health experts across the country that growing up affluent can be a curse as well as a blessing.

In the suburbs of major U.S. cities, the home of about 70 percent of the 3 million American families with annual incomes of more than $50,000, the curse seems to be getting increasingly destructive.

The rate of adolescent suicide has more than tripled in the United States since 1955, with even greater increases among white males in the affluent suburbs of Chicago, New York, San Francisco and Los Angeles.

In three villages on Chicago's North Shore "suicide belt," where 39 teen-agers took their lives in a recent 18-month period, the teen suicide rate has jumped 250 percent in the past decade and leads the rest of Illinois.

Drug and alcohol abuse among middle- and upper-class teen-agers has increased more rapidly than among the less wealthy. Sexual activity among unmarried white teen-age girls has increased more sharply than among unmarried black teen-age girls. Upper-class teenagers have increased their participation in extremist cults.

The statistics suggest an unpublicized, poorly understood misery that lives underground in the suburbs amid carefully pruned appearances. Respectable families try to keep the neighbors from knowing about drug abuse, family violence, even suicide attempts. But the parents and the teen-agers, the ones who survive, never forget the misery. And, for the most part, they'll talk only when promised anonymity.

Records of two teen-age suicide victims on the North Shore point to the tragic inability or refusal of parents to deal with adolescent suffering.

Billy K., 18, a graduate of New Trier East High School on Chicago's North Shore, smoked a lot of pot and took whatever drugs were available to him, according to the report of a community counselor.

The report continues: "His relationship with his parents was at best stormy. For a long period of time he was thrown out of his house, living kind of hand to mouth. His mother during this time would put $5 in the mailbox [of their $200,000 tree-shrouded home near the Skokie Country Club in Gelcoe] which he was to pick up between 5 and 5:30 p.m. when no one was home. This was to prevent the father and other members of the family from being upset with the sight of Billy."

On July 22, 1978, Billy hanged himself.

Paul R., a 15-year-old from a divorced family, completed a psychiatric evaluation in March, 1978, and answered questions about "what's troubling you most" by writing: "Worrying about school and if I'll pass my classes. Worrying about being accepted into different groups of kids."

After Paul took a shotgun up on the roof of a building near his home and shot himself in the head, his mother wrote a letter commenting on the suicide: "Paul hated school and he talked of quitting in December when he would have been 16. I told him he would not be allowed to do that and live at home. I did not feel he was serious."

In the Washington suburbs, a Kensington mother took her son's unhappiness and his pot-smoking seriously, perhaps too seriously.

She found marijuana in her 15-year-old son's room while he was off playing soccer. Confused, she took the pot to a police station and brought home a policeman to talk to her son. The boy refused to talk, outraged that his mother would turn him in. The policeman handcuffed and arrested the boy.

That was two years ago. The youth is 18 now, he didn't graduate from high school, and his mother fears he may never leave home. The mother, a college graduate and a self-described "fairly good mother," often wakes up in the night now, afraid her son and doubting herself.

Psychiatrists, sociologists, guidance counselors and juvenile court officials from affluent suburbs of Washington, New York, Boston, Chicago, Los Angeles and the super-rich enclave of Palm Beach, say that in the past 10 years they have seen a dramatic erosion in the ability of parents to control their adolescent childen, combined with an increase in social and economic pressure on affluent teen-agers.

The experts offer a confused and confusing explanation of why things seem to be going wrong for an increasing number of middle- and upper-middle-class teen-agers: parents are too self-centered, too caught up in proving themselves to give their children love and attention. Tyrannical peer pressure forces adolescents to either follow a stifling, conformist track to professional success or to chick it all, abandoning their ambitions to drugs, sex and self-loathing. Cruel economics mean that most affluent teen-agers, in an inflationary, slow-growth economy, will never be able to afford the kind of material luxury they now take for granted.

Any explanation that is simple is probably simple-minded, and beyond the mish-mash of reasons about why it is so tough to be young and affluent there is the inescapable fact that it is much tougher to be young and poor.

Rich kids do not suffer in silence. They are far more likely than their less affluent peers to receive psychiatric attention and other professional care. It is the poor, not the middle and upper classes, who are overwhelmingly responsible for teen-age deliquency and crime. Rich kids who do get into trouble with the law are far likelier to avoid criminal prosecution than the poor.

Dr. McKinley Cheshire, a psychiatrist and medical director of the Lake Hospital of the Palm Beaches in Florida, says the millionaire parents of his patients spare no expense in insulating their children from criminal prosecution.

"I know a father on Palm Beach who used a battery of three high-powered lawyers to get his kid off on a charge stealing of stealing hubcups," said Cheshire.

Robert Coles, the Harvard psychologist who has studied the children of migrant workers, Eskimos, Chicanos and the Appalachian poor, as well the children of the rich, writes that, by comparison, affluent children are "reasonably lively, competent, kind, thoughtful, imaginative, compassionate and 'happy . . . '"

But, for whatever reasons, a surprisingly large number of affluent adolescents, teenagers blessed with the best in education, health care and material comforts, are falling through the safety net that their parents' money provides.The consensus amoung the mental health experts who treat suburban teen-agers is that most adolescent failure begins at home.

For the minority of affluent teen-agers who wash out, the seeds of failure may have been sown in infancy, according to many psychiatrists.

The breakdown begins in the first few months of a child's life, when affluent, ambitious and busy parent do not take time to establish a presence for their child that is "consistent, continuous and caring," according to Dr. Eliot Soret, a cultural psychiatrist and assistant professor of psychiatry at George Washington University Medical School. The failure to establish that bond in infancy colors the trust that children have for their parents throughout their adolescence, Sorel says.

In Prisoners of Childhood, a new book about how narcissistic parents deform the emotional lives of their children, Swiss psychoanalyst Alice Miller writes that insecure, confused parents can strip their infants of the chance to ever develop self-confidence.

Miller says that infants have both a compelling need to be loved as simply what they are and "an amazing ability to perceive and respond intuitively" to what their parents expect of them. If an infant's parents deny him acceptance, the child will unconsciously attempt to become whatever he thinks parents expect (frequently a "good" child who never cries, gets angry, jealous or sad).

Miller, echoing the thinking of many child psychiatrists in the United States, says this can be very harmful when the child becomes an adolescent: "Understandably, these patients complain of a sense of emptiness, futility, or homelessness, for the emptiness is real. A process of emptying, impoverishment, and partial killing of his potential actually took place when all that was alive and spontaneous in him was cut off."

Dr. Sorel at George Washington University says this destructive parent-child relationship is nothing new, but that in the past it was partially corrected by grandparents and other members of the extended family who gave children love and acceptance. With the rapid increase in American mobility -- the Census Bureau says that half of the population moves every five years -- Sorel says the "correction emotional experience" offered by grandparents and other family members has fallen off sharply.

While it's impossible it isolate the precise causes of suicidal impulses and weak self-images among children, psychiatrists say they do see hazards in the increase in dual-income professional families and in high divorce rates.

According to a recent study by the marketing research firm of Yankelovich, Skilly & White, only 16 percent of all households now "fit the traditional concept of mother, father, and two children, with dad the breadwinner and mother staying home to care for the family."

Mental health experts say the increase in working women is a long-needed and healthy cange for American women, but that it can play havoc with child-rearing as married couples are forced to juggle the demands of bosses, bill collectors and housework.

The stress imposed on parents and children in these dule-income families is the major mental health problem in the Washington area, according to Burton L. Kraff, a psychiatrist and director of admissions at the Psychiatric Institute of Washington.

Caught between the conflicting demands on their parents, children in these families are frequently raised by a parade of "surrogate" parents -- servants or day-care centers -- that reduce the chance of a strong bond developing between parent and child.

"The crisis hits," says Robert C. Weigl, a social psychologist in the affluent Mount Vernon area of Fairfax County, "when the kids become adolescents and their parents find they have no control over the kid because they don't know him that well."

Psychiatrists, school officials and sociologists have always guessed that divorce, with the almost inevitable confusion, insecurity and guilt that it imposes on children, is potentially a major cause of adolescent unhappiness and delinquency.

A sharp increase in the American divorce rate, which the government says has nearly tripled in the past 20 years and which has cut across all socio-economic lines, means there are far more children than ever subjected to divorce-related stress. The Census Bureau says nearly 13 million children live in one-percent homes, and the total is growing by more than a million a year.

Whether parents are divorced or not, psychiatrists interviewed across the country say they've seen a marked decline during the past decade in the quality of parent-child relationships among many affluent families.

"I see parent who are refusing to be parents, who refuse to stand for something or say to their kids that there is right and wrong," says Dr. Bret Burquest, president of the American Society for Adolescent Psychiatry and a child psychiatrist who treats affluent families in West Los Angeles.

"So many of the kids I work with have no specific time that they have to come home, no restrictions on their use of cars or credit cards. When there are no limits, these kids get very nervous," Burquest says.

The nervousness begins, psychiatrists say, when a child grows old enough to appreciate gifts, and soon realizes that there may be no limits to what he can have. Many affluent parents assuage their guilt for not giving more of their time by buying oodles of toys.

"Children are indulged with trivia -- superficial material things -- and at the same time they are denied meaningful acceptance. There is no gut-level acceptance of children for what they are," says Dr. C. Gibson Dunn, a psychiatrist and medical director at the Springwood Psychiatric Institute in Leesburg.

The indulgence continues, Dunn says, as children become teen-agers, with parents giving their kids virtually everything they want except their time and "real standards of what's good and bad."

"The kids don't have to make any hard choices between the material things they want. They don't have to earn anything. They can have it all," said Dunn, who treats many affluent teen-agers from the Washington area.

He and other child psychiatrists say that troubled affluent adolescents appear as strangely hollow adults: they have grown up frighteningly fast, with a razor-sharp understanding of social status, money and sex, but without the decision-making standards to control their knowledge and toys.

"Kids grow up on the 10th story, but there is no foundation beneath them," said Dunn.

By the time they become 15 and 16 years old, a rebellious, troubled age under the best of circumstances, many affluent kids are "over-programmed" with athletic or cultural activities, have become a vortex of contradictory values, undisciplines impulses and an extraordinary pressure to measure up to the success of their parents, psychiatrists say.

"Parents think they are doing a good job to get their kid in as many activities as possible. I've seen kids run ragged going from dancing to etiquette to sailing lessons," said Dr. Cheshire in Palm Beach. "All these things reduce the kid's choice. The affluent child has less freedom than the poor kid. He doesn't have the opportunity to make mistakes and not catch hell for it. And all these programs involve authority figures, and the kid has less freedom to figure out who he is."

Harvard psychologist Tom Cottle says that knowingly or not many affluent parents are transmitting a dangerous message to their children:

"The parents are saying, 'I really think it is important for you to achieve, and when you do I'll think about loving you.' It is contingecy love. Love on the bonus plan. It should be love no matter what. When kids are 14, 15 and 16 the essentail bond is still with the parents. What I see is a fundamental disapproval of the way that kid is turning out."

On Chicago's North Shore, Ann Wood, a 16-year-old high school junior whose father is a professor of finance at Northwestern University and whose mother is a book illustrator, says there's precious little room for teen-agers to stumble, fail or even question the need to be a "success."

"It is not okay for us to be unhappy. No, you have to hold everything in. Conform. But even the littlest thing will break you up. Oh my God, I failed a test, will I make it to college? Oh my God, I broke a nail, what is going to become of me? What will my friends think?

"I find it very frightening. Frightening to make sure I have as many clothes as my friends, frightening to try to look richer than we actually are. If I reject all that appearance stuff, the only thing left is to get high all the time. There is no half way around here. Either you conform and look like a preppy or you become a 'burnout' and smoke [marijuana] all the time."

On Chicago's North Shore, as in many rich suburban areas, parents constantly compare the grade point averages, scholastic aptitude test scores and advanced placement status of their children, says Isadora Sherman, a family counselor in Highland Park, Ill.

One mother at a recent parents meeting said she was worried about the "social adjustment" of her son because he'd received fewer bar mitzvah invitations than her daughter. In April, when college acceptance letters arrive in the mail, telephones ring continually as parents call around to find out who's been accepted to the Ivy League colleges.

Many affluent suburban parents seem to approach child rearing as if it were a competitive sport, with the final score determined by their offspring's educational credentials and professional income.

"The abyssmal experience of being average with super-smart and successful parents puts enormous pressures on a teen-ager. The goals his parents set for him are often so far away that anything he can do will never measure up," says Dr. Dunn, at Springwood Psychiatric Institute in Leesburg.

"It is easy for a teen-ager to fall into the pattern of thinking that whatever I do won't measure up, especially if the parents are caught up in material things and their own career success," says Dunn.

Two North Shore parents, who agreed to be interviewed for this article only after a reporter signed a statement promising not to disclose their names or the village they live in, claim "it is very hard to raise average children here." ("Ordinary People," the Oscar-winning movie about tension in an affluent family, was filmed about two miles from their $250,000 home.)

"The average child is made to feel a failure," says the mother of three, whose husband makes $85,000 a year as a computer parts salesman. The parents worry about the intense athletic and academic competition facing their children at public schools. They also must put up with the carping of their 16-year-old who wants a car and says that his friends down the street gets to drive a Rolls Royce to school.

"We have one child who does very well in school and another who is not so interested. We hope we don't put these expectations on the children and we try to make the children feel good about themselves," says the mother.

The father says, however, that he would be ashamed if his sons turned out to be carpenters or plumbers. Both parents say that if any of their children became involved in drugs they would be made to feel "uncomfortable socially."

"Affluent parents suffer more than parents of the middle and lower classes when their kids don't do well," says Dr. Cheshire in Palm Beach. "They expect their children to behave better than the children of the poor. They feel more guilty, more embarrassed. . . ." Cheshire says that frequently guilt and fear of social stigma numb affluent parents to the critical needs of their teen-age children.

In Fairfax County, a couple that managed to raise two "wonderful" children has been humiliated, exhausted and victimized by the third. Their 18-year-old third son, whom they call "Richard the Terrible," wrote obscenities on a wall at Robinson Intermediate School and was kicked out. He stole whatever loose money his parents left around the house. His friends looked "like somebody who came out of the sewer."

He stupefied himself with drugs and liquor and was booted out of a psychiatric hospital after smoking pot in a detoxification unit. Richard has come around lately, stopped using drugs (after $30,000 was spent in three years on drug treatment programs), but his parents say they cannot forget their guilt, anger and feelings of impotence:

"I felt like after all we tried to do, how could he do this to us?" said Richard's mother, a real estate saleswoman. "Where have we gone wrong in raising him that he would do these things? We began to drop away socially. We didn't want to leave him alone here. We didn't discuss it with a soul at first. We were too embarrassed. There are other parents around here [a neighborhood of $110,000 townhouses] whose children are achieving and ours was not."

There is a narrow track to success in America's wealthy suburbs, according to the affluent teen-agers who are expected to follow it and the mental health professionals who treat those who get derailed. It includes good grades, high scholastic aptitude test scores, the appearance of wealth, a measure of athletic skill, acceptance, to a good college, acceptance to a good graduate school and success in a high-paying professional career.

"It's a masher," says Don Davis, who, as supervisor for court services in affluent Montgomery County, comes into contact with hundreds of juvenile delinquents every year. "It mashes the kids into a funnel. Their parents use all the mechanisms available -- schools, peer pressure, music lessons, pay-offs with material things and even psychiatrists -- to mash the kids into the success funnel. But the funnel is too narrow. It doesn't have any room for those who want to get off, look around or rest. It should be wider to show a kid how the rest of the world works."

Part of the squeeze on teen-agers in demographic. Seniors in high school next fall will have the dubious distinction of having been born during the last year of the baby boom -- post-World War II explosion of American fertility that began in 1946 and waned in 1964.

High school seniors, along with all their younger teen-age peers, live in the shadow of the greatest population bulge in American history. Like diners who show up late for the feast, teen-agers and young adults are likely to find many of the tastiest opportunities already gone.

"The last baby boomers will grow up into a world already too crowded for them," writes Landon Y. Jones, in Great Expectations -- America & the Baby Boom Generation. "Ahead of them, every base will be taken by their older brothers and sisters. . . . Throughout their lives they will face the prospect of salaries that were not quite as large as they hoped, devalued education, and difficult promotions."

The 1980 census found that the median age in America, the age at which half the population is older and half younger, is now 30 Accordingly, Madison Avenue has reaimed much of its pitch at the aging demographic bulge. Pepsi Cola no longer runs commercials "for those who think young." Middle-aged women like Natalie Wood, not pubescent California blondes, now sell skin moisturizer on television. Levi Strauss has blue jeans for a 30-year-old market that's thicker around the waist than the skinny and shrinking teen-age market.

Nowhere is the demographic squeeze greater than in the suburbs of Washington. "We've got many kids realizing that when they come of age they are going to be downwardly mobile," said Weigl, the social psychologist who works with families in Fairfax County. "Teen-agers think they can never measure up to their parents' earning power. It affects the kid's sense of regard for what he can do. They feel they are not worthwhile."

Exacerbating the pressure on teen-agers, according to school counselors, sociologists and psychologists, is a move toward conformity in public schools and increasing intolerance of teen-agers who don't share the values of their friends.

Isadora Sherman, who's worked with adolescents in the Chicago suburbs for 30 years, says that teen-ages there have swung from being "cliquish and conformist" in the 1950s to "kicking those values" in the late '60s to an "obessive concern with being successful" in the past five years.

A UCLA survey of 200,000 college freshmen over the past 11 years indicates that incoming college students are increasingly materialistic and conformist. In the past decade, the number of freshmen who said they are interested in being "well-off financially" doubled.

In affluent Westchester County, near New York City, an increase in suicide and drug abuse among affluent teen-agers has dovetailed with a similar move toward conformity, says George Nash, a sociologist and director of research for the county mental health program.

"The Hippies provided us with a safety valve," says Nash. "Now we have gone back. We are working harder. We are going to graduate school. We are all on the right track. We are the moral MBA majority. Parents who have had to work hard to become and remain affluent are not very understanding. They say we are all agreed that all this foolishness [of the 1960s] is over and done with. We all have to knuckle down."

Adds Nash: "The kid who doesn't fit in has no place to go."

In Fairfax County, Vincent Picciano, director of juvenile court services, sees the same straitjacket conformity.

"We are talking about increasing controls in the high schools, a lot more pressure. Economic constraints put on pressure to succeed in school. As things get tighter, kids either conform or react. They react either aggressively against others or against themselves," says Picciano, who's worked in Fairfax for 20 years.

On Chicago's North Shore, Lisa Davis, a 15-year-old high school senior, says many students are panickering.

"The reasons for the suicides and the drug use when you get right down to it is that kids want to rebel, but they don't know how the hell to escape. There is a dictatorship of peers. You have to have a tan, clothes, good grades. And if you don't measure up, you can't escape."

"When a kid begins to get rebellious, his grades suddenly drop in school, he refuses to do anything around the house, parents must realize there is a very serious problem, probably drug-related," says Dick Hayman of Great Falls, Va., the father of two children in their early 20s, a daughter who went to college and "turned out beautifully" and a son with a history of drug abuse and drug-related offenses.

"Many parents wait too long, until the kid is too far gone to be helped. I wish I knew the answer for what a parent can do differently, except try to get to know the parents of his children's friends, find out their values and to try to maintain a framework of rules in which the kid can operate. Kids want to know what their do's and don't's are, otherwise they walk around feeling lost," says Hayman, an administrator with the Office of Personnel Management and the chairman of a group attempting to bring a home-based drug treatment program to the Washington Area.

For affluent teen-agers, especially young men, who either haven't the aptitude or the interest in traveling the narrow track through college and into demanding professional careers, there is growing pressure literally to get lost, according to Harvard sociologist David Reisman.

"There's a relatively small but absolutely large number of these young men don't go to college. Who take menial jobs or just wander around. No one seems very interested. They are not obviously deprived, but they are obviously unhappy," says Reisman, the well-known author of several books dealing with affluent society, including The Lonely Crowd.

Reisman says that Hinckley, the accused assailant of President Reagan, fits the pattern of young men from successful families who fail to measure up to a standard of academic and social achievement and drift off into their own isolated worlds. Hinckley, like other sons of wealthy parents, received sufficient money from his parents to keep wandering.

There are no statistics on how many of these wandering sons of privilege there are across the country, but interviews with mental health authorities in six major metropolitan areas indicate the problem is common.

On Chicago's North Shore, in the Washington suburbs and elsewhere, according to psychologists, counselors and high school students, there's no room for these "failures." They are looked down upon and urged to move on.