ANNED AND IN HIS tennis whites, Peter Duchin ambled slowly forward through the gorgeous chaos of the Robert F. Kennedy Pro-Celebrity Tennis Tournament at Forest Hills.

It was the 10th anniversary of this particular rite of the rich and famous, a day-long ritual which is tuned to the hum of recognition.

Clouds of autograph seekers hover around the stars and their retinues: the conversations under the striped marquees take place between faces that seem strange in three dimensions after overexposure in two.

Peter Duchin had just finished a match with Oleg Cassini and was on his way to another with Julius Erving. There were a few clicks from nearby Instamatics, and then there was a small autograph book, the kind that usually has, as this one did, a 12-year-old girl with a gigle behind it.

"Wait a minute," said Dalixy Laracuente of Staten Island, after Duchin had signed her book, "Could you make it say 'God bless you'?" Duchin made it say God bless you. Dalixy walked away, only to dart back, quick as a minnow, through the crowd. "Wait a minute," she said. "Who are you?"

"I'm Peter Duchin," Peter Duchin said. Dalixy reserved the next question for a nearby jury of her peers."Who," she asked them, "is Peter Duchin?"

She was greeted by an eloquence of shrugs. There is too much tabula rasa in a 12-year-old to account for Peter Duchin, for much of who he is has to do with evocations rather than explanations, and evocations mean little in lives with so much more future than past to them.

But for those who dwell in a world where such things have value, Peter Duchin is, as one observer put it, the Gucci of the society orchestras, what New York publicist Robert Zarem describes as "the final stamp of elegance - in a certain sphere, in a particular realm, in a certain area, his is the first name that comes up."

It is, in fact, the music of that certain sphere that is Duchin's domain, and the realm in which he performs is the one in which the debutante, the socialite and the chairman of the charity ball hold forth.

He plays conventions as well - the meetings held by Braniff and Avon and General Motors and the one the Democrats convened to nomiate Jimmy Carter, and dozens of ones in between.

He is the society musician whose price can go as high as $10,000 an evening, he is Jacqueline Onassis' escort, Averell Harriman's godson, and he is the son of Eddie Duchin, pianist and bandleader of the '30s and '40s who gained as many fans through the sentimentalization of his memory in the "Eddie Duchin Story" as he did playing the "Nocturne in E Flat" in the grand ballrooms of the great hotels.

As Eddie's son, he is the keeper of the keys to a singular and long-enduring memory of romance, one that featured long evenings of silk and satin and the gleam of a gold cuff link in candlelight, of polished manners and polished floors, and of intricate flirtations so utterly alien to the hard bargains of the singles bars.

And as Eddie's son, he serves as well, in some circles of America's rich, as the custodian of custom and ceremony. "You could say," he said in his big bright house in Westchester that sits at the end of a linden-lined drive. "that to some extent, it's a security thing. The people I play for can say, 'Peter's doing what his father did.' That can be very important in a relatively young country.It wouldn't mean that much in Europe, but it means something here."

It means that debutantes whose mothers danced to the music his father played now also dance to a Duchin, now that debutantes are having parties once again instead of giving the money to housing projects in Newark.

It means that every year he plays for former Treasury Secretary Douglas Dillon's nonagenarian father on his birthday, marking that anniversary for the last 10 years as he marks a handful of others - the signed contracts coming back (with their 50 percent deposits) from some of those who have kept faith with tradition with handwritten notations - "this is the 10th year you've played for us, the 12th, the 15th . . ."

But it also means that despite the easy rhythms of a life that waltzed him from Hotchkiss to Yale to the mansion in Westchester, despite the moneyed wife, the three children, the safaris in Africa and all the other graces of a life that seems to have no corners to it, there is just the faintest whisper of discontent, just the slightest shadow of regret that it can be difficult at times for a society bandleader to be considered a serious sort of person. Jackie O and the Truck

Slouching on the couch with determined nonchalance, only his eyes betraying a polite wariness, Duchin sits in the living room surrounded by the eclectic catch of his travels abroad - pre-Columbian pottery from Panama, Eskimo sculpture from Alaska, a totem from New Guinea. The totem is a rather fierce-looking object which, Duchin explains, is brought out by the tribe back home for special and ceremonial occasions. Duchin himself is looking very casual, dressed in the basic country uniform of khakis, T-shirt and shoes without socks, his hair in that style that is sort of blown-about Kennedy casual.

He is telling a story about playing the Swan Ball in Nashville and how "three or four members of the Gucci set down there " wanted to know if there was anything they could do to make him comfortable. He asked for a pickup truck and some country and western tapes for a lawyer friend of his, whose birthday it was and who had come down to see the Grand Ole Opry.

"They couldn't believe I wanted a pickup truck," he says. "They have some image of me as some sort of stuck-up society guy who spent his life taking out Jackie Onassis."

He is, in fact, not at all stuck-up. He is affable and slightly overweight, with the glossy good looks of the sort of person featured in a Dewar's Profile (Last book read: Joseph Conrad's "Nigger of the Narcissus." Ambition: "To have a lasting effect on the arts situation in this country.")

He salts his conversation with a good-natured, self-deprecating sense of humor and a collection of determinedly hip expressions that sound, paradoxically, dated. He is 41 now, the same age his father was when he died of leukemia. He is asked what it is he wants for the future, what with the present streaming along so pleasantly.

"I find it very hard to think about the future," he says. "Life has become so harried. People are talking about such narrow specializations." There is a pause."China." he says. "Wouldn't it be a gas to play China?" 'All the Giants Were There'

In 1961, he was playing the Maisonette Room in the St. Regis Hotel and living above Carnegie Hall. Bobby Short was his neighbor then, and one late night near Christmas he asked Duchin to come by and meet a few of his friends.

Gathered in the living room as the snow fell outside were Leontyne Price, Mahalia Jackson and Odetta. They sang gospel Christmas music long into the night and Eddie Duchin's son just "sat there in awe."

"Being in the right place at the right time is very important in life," said Peter Duchin. At times, it seems he has always lived in that placed.

They called Eddie Duchin's marriage to Marjorie Oelrichs, the sugar heiress of n New York and Newport, the wedding of Park Avenue and Broadway. She died six days - after her son was born. A set of glittering connections was the legacy she left him, and they are with him still, enduring like a fine old silver service.

Mrs. Averell Harriman (Harriman's first wife, Marie) was a very good friend of Mrs. Eddie Duchin, and it was the harrimans who cared for her son until his father remarried when Peter was 11. It was Mrs. Harriman who arranged for a charity fund-raiser to be held at the St. Regis the very night he opened there and "everybody came," as he remembers now.

"The Whitneys, the Rockefellers, all the giants were out there." It was his first job out of the Army.

Mrs. Hugh Auchincloss was also a good friend of Mrs. Duchin, and when Mrs. Auchincloss' daughter married John Fitzgerald Kennedy, another circle was completed.

Duchin is reticent about the famous he knows: he proffers no personal stories, but he mentions their names the way an elegant woman wears a good perfume - discreetly, just enough to have an effect without overwhelming the others in the room.

"Averell's" name is sounded like a church bell, at regular and dignified intervals. Henry Kissinger requires just the slightest tug to fall into the conversation.

All in all it seems a rather tricky role to play, half guest, half hired hand, a part of the world for which he provides the background music. It is not, Duchin said, something he thinks about much.

There is a certain level of society, he said, "that doesn't change. The Astors, the Rockefellers, the Harrimans, the Engelhards . . . you can have a lot of money and never be a part of that world. They talk to a lot of people, but they're not all included. They take their world absolutely for granted."

And how do they take them? "They probably feel more comfortable with me," he says simply. "They don't have to worry about my comportment and behavior, about whether I know how to act."

Does that mean his role then is that of musician to the court?

"If I'm a court musician," he says just a bit tersely, "then so is Lenny Bernstein." 'A Way to Earn a Living'

The photographer asks Duchin to sit at his piano for a picture. Duchin sits down, leans forward, props his elbow on the keyboard, cups his chin in his hand and assumes a photogenically coy expression. It is clear that the hours spent posing for publicity stills has made the response automatic.

He talks, meanwhile, of meeting heads of state of vacationing with senators, but it is not grandeur, he says, that impresses him. He is asked what does. "Truth," he sayys. "Honesty. Reality." And, finally, creativity. "Creation," he says, "impresses me."

The permanent results of his own artistic creativity are not extensive. A book of Christmas carol arrangements. A jazz ballet on which he has been working sporadically for the last several years. A couple of Broadway scores that have not been produced.

At Yale, says Zarem, a fellow alumnus, Duchin was "an extraordinarily serious musician who seemed to be on his way to being a serious composer." But he was also, Zarem says, "very much a loner - he had a history and a background no one else had. It was a difficult thing to share with people."

"I didn't want to spend my life sitting in a loft," Duchin says of his own change of heart. "If you like people and relate to them and care for them, then what I do is an exciting way to earn a living." Mamma Remembers

Much of what Duchin does is presided over by the general manager of peter Duchin Orchestras Inc., Otto Schmidt, who operates out of both New York and Florida by way of a well-thumbed flight schedule.

There are about 100 musicians who play under the Duchin aegis in varying groups and arrangements, and Duchin himself plays about 150 dates a year, about a third of them conventions, a third charities and a third debutante balls, private parties and weddings. Schmidt is reluctant to quote exact prices, but $7,500 - $10,000 for an evening of Duchin and his orchestra seems standard.

There are bookings into 1985. They have played 39 states in the last few years. And while there have been certain changes, Schmidt said, there are certain verities as well.

"Now disco's the thing," he said, "all the time, there's something. But I'll tell you one thing, the same families are giving the same parties. And they know Peter Duchin always shows, and it's always the same. It's as if you bought a good automobile or had a good hairdresser. The name means quality."

Otto Schmidt has been Duchin's manager from the beginning. Once he was a saxophonist in another society band, Ted Straeter's orchestra, and it was Straeter who lent Schmidt to Duchin when he first put a group together back in 1960. Schmidt played the Persian Room, the Copa, the Plaza; he knows a thing or two about continuity.

"When you take a name like Duchin," he said, "you're on solid ground. World War II, pre-World War II. Eddie Duchin was a big band name, everybody of that era knew Eddie Duchin. Ten, 15 years later, mama remembers. It's her daughter's turn, and she says, 'Maybe we can get Peter Duchin.' The deb, she sees his picture; she says, 'Oh, is he that handsome young guy?' The older guys don't have to worry that he's one of those snotty young kids. He's not Chicago. Mama is happy, she knows he'll play songs from the old era, and the youngsters know he isn't some corny society guy."

And as surely as the seasons change, debutantes become socialites, and in such lives, Schmidt believes, some things don't change. "In any town, I don't care where, if your husband's going to make it, you got to be a doer. American Cancer is very good, whatever, but you got to join a committee. You're not going to get your picture in the society pages for nothing. These people who are already established, they're going to say, 'I'll only be chairman if it's done right - the right food, the right flowers, the right country club, and Peter Duchin."

Martha Hyder heartily concurs. Well-ensconced among the upper reaches of the socially prominent in Ft. Worth, Tex., she was chairman of that city's quadrennial Van Cliburn Competition. When Neiman-Marcus agreed last year to transform the opening of its new store in Ft. Worth into a benefit for the competition, Duchin's was the first name she thought of to do the musical honors.

"We wanted to give it that certain style and elegance," she said. "Of course, there are other good bands, but they don't have quite the name when you're trying to sell tickets. Peter Duchin is a drawing card all over Texas. And you've got to have a good one when you're trying to pull people from the beach in August. They know that if you're going to spend that kind of money to get Peter Duchin, the rest of the party's going to be pretty special too."

Part of the appeal, she said, "is that he grew up in Averell Harriman's home" - that's important in the East anyway; it makes him one of Them - and part of it is "his father, of course, he brings back a lot of memories." 'All That Glamor'

Otto Schmidt is well-versed in the memories. He's no sentimentalist, not the type to linger long in the darkened alleys of the old days, but he knows well the era that the Duchin name recalls, and on request he'll play a graceful arpeggio on the past.

"Back then, you know, it was wonderful, to see all the names you wanted to see - it could take you a week! There was Dorsey at the Pennsylvania Room, Miller at the Statler, Eddie at the Waldorf, Ted at the Plaza. A young guy with his date, even with all that glamor, he could go for 20 bucks or less.

"That era is gone now," he said, "it would cost too much. But it was very romantic. I would go to the Plaza and it would be so beautiful, I would cry, me - I was in the business myself. But those guys, when they wrote those beautiful love songs, they were in love. If a guy's got a heart, he's going to write a tender lyric. But then, all of a sudden, it stopped. It was just notes, no one was paying attention." 'You Could Start a Revolution'

Peter Duchin Orchestras Inc. pays attention. Schmidt keeps one ear cocked to the radio whereever he is, ready to slip a soon-to-be-popular song into the repertoire as soon as his instinct tells him it's about to be hot. The Duchin musicians must keep a vast repertoire of songs under their control, from "String of Pearls" to "Honky Tonk Women," and there are new and often exotic additions all the time.

Sometimes it's easy. During the Democratic Convention, they had a man with a headset on keeping an eye on the door through which Calfornia Governor Jerry Brown would make his entrance. Instructions were radioed up to the band to strike up "California, Here I Come" the minute he appeared.

Sometimes it's not. "You don't have to be a genius to play 'California, Here I Come,'" Schmidt said. "But when you play the U.N., you have to know the official songs of each country and sometimes the poor ambassador isn't sure things change so fast. You check with National Geographic, whatever, but you must be prepared. Some weird country someplace, you could start a revolution playing the wrong thing."

The research is brought into play not only for the celebrations of nations but for the more personal rites of passage that mark the living of any life. "We play a guy's 80th birthday, we're going to research the music he heard in 1928. It's probably the first time he's heard 'Barney Google' in a very long while," Schmidt said. "If it's a couple's 50th wedding anniversary, we play the waltzes they courted to, and I've got news for you, that is a very big deal for them."

For the young, at the debutante parties and the college proms, there are Elvis Presley medleys and the mindless measures of disco. The occasions themselves are as varied as the places in which they're played - June and December are the busiest months, but October alone has 17 dates - a concert in Atlanta, a charity ball in Denver, a private party in Memphis, the Junior League in Harbingen, Tex., and there are dates in Little Rock, Los Angeles, New York, Utica, each with its own set of variables, its own moods and memories to be orchestrated and played upon.

Duchin knows when to play down his own role, when to be "very background," the discreet musical accompaniment to whatsoever social ritual requires his presence. But at the conventions, those desultory gatherings of groups of people bound together only by the rather tenuous tie of a common employment, he is the performer, the entertainer, the star.

It is at the conventions, Duchin says, that he gets a sense of what is going on in the country, and it seems that the observation of people going about the mundane tasks of buying, selling and trying to make it provides something of a reaity check to the rarefield atmosphere in which he lives.

And it was at a convention, Duchin says, that he gleaned a clue to the probable fate of Sen. Edmund Muskie's presidential ambitions. "It was at a convention of newspaper editors and publishers in Atlanta," Duchin said. "There were 30,000 people there, and I knew Ed Muskie was the same hotel. So I said to the guys who were running the thing, 'What if I got Ed down here and introduced him and he could work the crowd a little?' They said sure, so I called him and he said he was too tired. I knew then that he would never be president." 'Did You Hear That?'

At the Pro-Celebrity tournament at Forest Hills, Duchin and his wife Cheray are sitting in the shade of a striped marquee talking to People magazine photographer Henry Grossman who suddenly asks the kind of question that's bound to buy a round of smiles when there's a reporter's notebook on the table.

"Peter," Grossman says, "are you too young yet to think about going into public office?" Duchin says something to Grossman about not being interested in elective office but that some sort of government appointment had crossed his mind as a possibility for the future.

"You are so qualified and so interested in so many issues," Grossman says, "and with the connections you have it would be a sin for you not to look into what kind of office would use your talents to the fullest, and then go out and get it."

"Did you hear that?" Cheray Duchin says to her husband. "Did you hear that? I may not be able to quote Henry exactly the next time we talk about this, but I'll remember what he said."

Duchin worked on Robert Kennedy's campaign for the presidency, and he has played for a host of Democratic hopefuls trying to raise money. He played the last Democratic Convention and the Inaugural. He has been on the Yale Music School's advisory board, and a director of a drug rehabilitation center, and he is a member of the Concerned Citizens for the Arts and the Arts Council of New York. He deplores the lack of commitment in the '70s and mourns the passing of the activist '60s. He thinks the SALT talks are of "absolutely overwhelming importance," that the government is bloated, and he was very concerned about the Panama Canal. And yes, he realizes that a lot of people consider leading a band something of a lightweight profession.

"People sometimes don't realize how important entertainers are to politicians," Duchin says. "But when I'm doing a fund-raiser, people say, 'My God, Peter Duchin's playing for him?' - that's big bucks. It's very important. It sure draws a lot more people than some political scientist talking." 'It's Tough, This Business'

The night before the tennis tournament, there was a very private party at the Rainbow Room for the professional tennis players and their celebrity teammates. The music was provided by Peter Duchin Orchestras, and because it was the 10th anniversary of the tournament, Duchin himself played, even though he was there as one of the invited guests.

Also at the Rainbow Room was Denny LeRoux, who wears neatly tailored denim, in contrast to the formal dress of the rest of Duchin's band. LeRoux was the one who sang the Elvis Presley medley and the disco numbers and he brought along several copies of a song he's recorded to give to whoever might be interested.

LeRoux has played for Duchin for eight years. He is 30 years old and came to Duchin's band after scuffling around New York City with a number of rock bands that had lives as long as May flies. He had never heard of Peter Duchin until a friend's father got him booked into a society ball that Duchin was also playing.

"I'm a middle America kid myself," LeRoux said. "I walked in and saw the band and thought, 'Gee, this is weird. Oh wow, tuxedoes, look at this.' But I began to realize that music is music, and what Peter does he does very well."

Besides, LeRoux has ambitions. "I want to be an established entity in the music business," he said. And that is going to take a lot of doing. So far it has meant a lot of long nights in small planes going to out-of-the-way places in Connecticut and New Jersey at his own expense to convince radio stations to play his record. "It's tough, this business," he said. "Really tough."

It was not so tough for Peter Duchin. "That's showbiz," said LeRoux. "I'm a realist. I try very, very hard not to alienate anybody."

And that, he said, is one of the many things that is so great about playing with Peter Duchin. "How else you gonna get to play a party where you meet somebody and you say, 'Hey, know anyone who'll play my record?' and he says, 'Yeah, my cousin George. He owns Japan and 400 radio stations.' And you say, 'Great, can I give him a call?'" 'The Key Is Flexibility'

"I know how to play for society and for all the other groups I play for," Duchin says as he brings forth a brief shower of jazz from the piano in the living room. "If they care about the occasion, and if they're paying for me they do care, then music can make or break a party. You have to know how to watch and create the mood."

You have to know, he says, when to speed it up and when to slow it down, when to play to memories and when to play to romance. You have to know when to bring the female singer (definitely not at the wedding) and when to hit the rock 'n' roll (very good at debutante parties, not so hot at 50th anniversaries).

And always, he says, the key is flexibility, having the capacity to skim through decades of musical taste as if they were grace notes, and the comfort is knowing that no matter what the changes in the tenor of the times, the song most often requested is and has always been, "As Time Goes By."

"It's great," he says. "A chick of 16 will come up and ask for that."