When Diane Moore and her family were assigned their three-bedroom apartment at the Potomac Gardens public housing project, she felt privileged. There was cause for hope.

It was 1967 and the project was fresh and new. "I remember the lady at the housing office told me, 'You're one of the chosen few,'" Moore recalled. "I believed her then and I felt good. But she lied to me."

Potomac Gardens, on the southeastern finges of increasingly affluent Capitol Hill, has not turned out to be the promised land Moore had hoped it might. It is indifferently maintained and has aged without grace. Concrete walks have crumbled, rubbish and shattered glass litter courtyards, laundry room machines are broken down, paint is peeling and plaster falling.

Yet, it is not nearly so much the damaged buildings that worry Moore as the damage and the stigma she fears her children are suffering because they live in the project.

"When I moved in here I had beautiful kids," she said. "Now, one by one, they're getting into trouble and I'm dumbfounded. I don't know where to turn next."

Moore's cry is echoed everywhere through Washington's start National Capitol Housing projects. Far more than they worry about the basic fact of being poor, concerned mothers like Moore brood about the influence of "surroundings" or "the other kids" or what the social workers term "peer pressure" on their own children.

Frederick Saunders, assistant director of the D.C. Recreation Department's Roving Leader Program, has spent 15 years working with Washington's poor youngsters, most of them black and most of them from the projects.

"I don't think poverty itself is the number one problem," Saunders said during an interview in his cluttered office at Chillum Place NE, near Washington's eastern boundary. "Poverty could be the inspiration our kids need, if it was used right. But peer pressure is really rough. Many youngsters are too weak to say no when their friends challenge them to steal a car, snatch a purse or hustle dope."

Moore's children aren't in that depth of trouble, but she frets, especially about the boys. She's not sure how much longer she can influence them "to do the right thing."

Moore, who is 35, has six children. The eldest, Duane, is an 18-year-old high school dropout. "He's supposed to be working at a car wash nearby," his mother said. "But sometimes he works and sometimes he doesn't."

Her 15-year-old son, Mark, is on probation for beating up another boy at school. "Mark's girlfriend said this boy had hit her and so Mark went and hit the boy and he filed charges," Moore said. "Now Mark has to see his probation officer for six months and if he doesn't get in any more trouble he'll let off."

Moore let her thoughts ramble over her concerns for her children one recent evening as she and four visitors sat in her small, chocolate brown living room, one wall of which is covered with mirrored tiles in an attempt to create some illusion of space. In one corner stood a small TV set ("bought for $25 at Goodwill") and in another a record player ("a gift, just like my dog, Gigi").

"I really worry about these kids a lot," she said. "Like Duane, he asks for things I just can't afford to buy him. So I worry that one day he'll just snatch a purse. He knows other kids do it and get away with it. So maybe he'll do it, too. I worry about that."

Moore took obvious pleasure, in the efforts of her 16-year-old son, Joseph, to work toward a career in computer technology. Joseph is enrolled in a new program called Experience-Based Career Education, an alternative to traditional classroom work. Quiet and neatly dressed, he poured tea into yellow cups for his mother's guests as she spoke.

But she worried about all her children, Moore said, with regard to the labels she believed were attached to them. "Why do people in public housing have to be branded as all bad?" she asked rhetorically. "Why do our kids have to be called Project Kids, Welfare Kids?"

This kind of despair is heard often from project mothers, especially those striving to guide their children through a semblance of normal live under strained conditions. They complain of the popular image of the projects as crime-infested. They complain of journalists, perhaps well-meanings, who portray the projects as sinkholes, because such images hurt their self-respect.

For Moore, perhaps more than some other project mothers, there is an extra measure of distress, of bitterness, about the way she and her children live. "I grew up in a private house," she recalled in a tone of quiet pride, and I didn't know there was such a thing as public housing until I was an adult."

She was one of six children, Moore said, and all either completed high school or, as in her case, had some kind of technical training. Added to her concerns is the feeling of having taken several steps backward and the worry about whether she and her children will ever be able to regain that lost ground.

Like the vast majority of mothers in the projects, Moore must face these worries alone. Whether because of divorce, as with Moore, abandonment or just never having been married, women tend to be the sole unifying force among the poor black families of the city's projects.

Thus, "public housing families" and "welfare mothers" are synonymous in the public mind.

How does a welfare mother manage?

"You rob Peter to pay Pual," Moore answered with a faint smile.

"Yeah, but Peter never gets paid and Pual is always hollering," added her sister, Creola Whitaker, a heavy woman who walks with the help of a cane.

Then, more reflectively, Moore said, "you don't rally manage. You just coast along. It's hard. We depend each other, on our friends." All in the stuffy little room nodded.

Moore receives $489.60 a month in Aid to Dependent Children. Rent for the apartment was just raised from $79 to $85. For $134 she receives $274 worth of food stamps.

Foods, she said, is her single greatest expense. "After the stamps I guess I spend between $60 and $70 a month on food," she said. Glancing at Mark, who weighs 250 pounds and has ambitions to play football, she smiled and said, "These are eatin' children."

The pressure of feeding and housing a large and growing family in cramped quarters showed plainly in the apartment, despite Morre's evident efforts to keep things neat. Down a narrow corridor off the living room, restaurant-size pots and plans spilled out of beige cupboards onto the floor.

"When we moved in, in 1967, we had five kids and we had enough room in this apartment. But now there's six children and me and there just isn't enough space." According to regulations, project families are not supposed to have more than two children to each bedroom. But at a Potomac Gardens, three-bedroom apartments are the largest.

"Oh, I've applied for a larger apartment at another project," Moore said. "And they tell me that I'm eligible for one. But that's all they ever say."

At the end of February, there were 8,001 names on the list of persons awaiting project apartments, according to Mary Kay Favinger, occupancy officer of the District Office of Housing and Community Development. Thus, while project people themselves are full of misgivings about the places in which they live, many of Washington's poor would gladly change places with them.

Moore has tried to break away from the projects and her reliance on welfare, but each time, she said, she's been thwarted.

"Four years ago, I was working as a file clerk for the Veterans Administration," she said. "But I couldn't make it because my (welfare) payments were cut and the rent was raised.

"My youngest daughter wasn't in school then and I found I couldn't afford to pay for a baby sitter. Once, for half a day, I left the kids alone and the next day I received a warning from the housing authority." Regulations prohibit children under 16 of welfare mothers from being left at home without supervision.

So," she said with a small sigh, "I realized I had no choice. I had to go back on welfare."

At another public housing complex, Kenilworth Courts, on the eastern tip of the District, fewer than 25 families living in the 422 u nits have men heading them. Yet, according to Kimi Gray, a longtime resident with encyclopedia knowledge of the project, no more than 35 percent of the families are on welfare.

"I know some folks would find that hard to believe," Gray said, "but that's just because all public housing people have been branded, lumped together, by white people, Congress, all those psychiatrists and the newspapers."

"And that's funny because it's them who've thrown us together in places like these, without incentives, and it's them who thrown us some bread crumbs from time to time. And it's them who give insufficient funds to all those programs and then say the programs are failures."

Gray, who "was born in a project myself and am unfortunate enough to have to raise my five babies in a project," tends to be protective of the people with whom she lives.

Yet, conditioned by a lifetime of contact, with social workers and an array of welfare personnel, she conceded that "peer group pressure" is the prime cause of difficulty for mothers and children who are trying to stay out of trouble.

"If you bring home books from school, then you're a punk," she said. "You can't study because you're supposed to be out on the basketball courts."

But, she insisted, there were "good kids, lots of good kids," in Kenilworth Courts and in other projects, too.

"No one says anything about the good kids," she complained. "No one writes about the young girls who don't get pregnant, about the young men who graduate and go to college. No, all we hear and read about is crime, about all those illegitimate babies.

"The newspapers only write what the public expects and wants to read. And that hurts more than it helps.

Just who can help, who has the ability and understanding to offer genuine help to project families searching for it, is remarkedly difficult to know. Despite the proliferation in Washington of federal and local government agencies and private groups committed to aiding the poor, few families seem to understand how to make use of available services.

At the same time, some of those within the agencies, however sympathetic they may be, have grown skeptical about the will of project people to help themselves.

Roving leader Frederick Saunders is a case in point. Saunders, 40, grew up at the Barry Farm Dwellings in Anacostia. "I didn't know I was growing up in a ghetto," Saunders recalled. "My mama hid a lot from me. As a result, I've always had a sense of hope."

"But now, it's become a major goal among poor black folks to get into public housing, rather than trying to get out of it. Receiving welfare, public housing, public assistance of all kinds has become a cause of celebration instead of a stepping stone.

"Very few of us are prepared to use adverse conditions as stepping stones. Most of us just use them as excuses."

Kimi Gray doesn't accept that judgment. She's been on and off welfare most of her life, she readily states, "but I don't like to accept anything from anyone and I fall back on welfare only when I have no choice, when I can't do anything else to survive."

Gray's lifetime of experience in the projects and with the welfare system has convinced her the only help that really matters to Washington's poor blacks is self-help. And that kind of help, she indicated, can mean more when it's accompanied by a touch of gentleness, a human touch, rather than just money.

This sentiment helped give rise to a Kenilworth Courts program called College Here We Come. Gray and a handful of Kenilworth women began iit in 1974, "right here in this living room" she told a visitor recently. "So far, we've sent 108 young people from Kenilworth Courts to college."

What did she mean by "sent"?

"I mean there are some good kids out here whose parents can't afford to send them to college. So we get them to take the correct classes in high school, we check on their behavior, we go to their graduations, we help them pay for the caps and gowns if necessary, we help them apply for entry, we help them line up summer jobs, we pack their trunks and we put them on the bus and once they get there we help them get scholarships. If that ain't 'sending' them, I don't know what is."