THE COFFEE SHOP of the Hotel Washington is an unlikely retreat for powerbrokers. The ambiance is plain and folksy - greenery plunged formica nests, its Jujubes-like orange and green decor jarring to early morning senses. Yet, this airy room with its view of the granite bulk of Pennsylvania Avenue is where Mayor Marion Barry and his roundtable of advisers frequently meet.

Barry usually chooses a table that keeps the District Building in full view, and manages a steady rapport with the unobtrusive waitresses. Here work gets done.

Every politician has a hideway, every political personality an inner circle. Be the tightly-knit group of friends and advisers called the Kitchen Cabinet, the Georgia Mafia, or simply, cronies. Favor-seekers hound the group, quick to identify the insiders and attempt to cultivate them, forcing the inner circle to build a wall around itself. Determined to keep the fragments of the old, open style Barry has had with his friends and advisors, the mayor often attempts to escape the trappings of the District Building.

In the coffee shop, Barry confers with his two closest advisers, Ivanhoe Donaldson, the astute, blunt general administrator, and Herbert Reid, the scholarly, relaxed legal counsel. It was just across the hall in the hotel's restaurant where Barry caucused about his plans to run for mayor with his closest personal friend, James Palmer, the soft-spoken, moderate senior chief deputy in the U.S. Marshal's office.

Barry brushes aside the notion of an inner circle. "I have several circles," he says, impatiently. "Some people are in one of two circles; one is a strictly governmental circle, there's a general circle, and I don't have a broad personal circle."

Whatever the scope, Barry's definition of friendship is trust. Courtland Cox, an ally from the 1960s civil rights movement, who was brought into the administration, explains, "Marion trusts people with the same frame of reference. With those people he says 'I know your sense of judgment, we have been through a problem before.'"

Barry, however, his bushy rocket of eyebrows raised in concentration, managed to name to the inner circle every single one of his appointees. Pure politician. "There is a strictly governmental circle, by and large, Ivanhoe, Elijah Rogers, Judy Rogers, Gladys Mack, and to some extent, Colin Walters, Carroll Harvey and Dwight Cropp. In general, Herb Reid," says Barry.

At the same time, Barry has a coterie of personal friends, who emerged into occasional political advisers, including Thornell Page, the state director of the Cooperative Extension Service at the University of D.C.; Lorraine Whitlock, a retired school teacher; John Wilson, the D.C. city councilman, now trying to redefine his role as the legislator and Barry's as the executive; Audrey Rowe, special assistant for Youth Affairs, and Lilian Adkins Sedgwick, a state Democratic Party official, now a general special assistant for Barry. In the reverse order - from political contacts into personal friends and advisers - Barry includes David Abrahamson, the advertising executive; Delano Lewis, the C and P vice-president who served as head of his transition team; Nancey (Bitsy) Folger, a fundraiser, and the Rev. Philip Newell. "Much of it overlaps," says Barry.

But this is how it lines up in private. For the Super Bowl game, just two weeks after his inauguration as mayor, Barry called up a dozen friends to watch the game. Those who showed up included Herb Reid who also sits in on the sometimes high-stake Barry poker games; Max Berry, an attorney and art collector and Barry's campaign treasurer; Jim Palmer; Sybil Hammond, his appointments secretary; Bitsy Folger, and the Rev. William Wendt, one of the city's most socially active ministers. "I rooted for Dallas, Barry for Pittsburgh, and all his staff rooted for Pittsburgh," says Jim Palmer, laughing. "I guess that shows their loyalty."

When Walter Washington was first appointed mayor in 1967, his inner circle was a triangle, embracing attorneys Charles Duncan and Julian Dugas. The Dugas bond with Washington dated back to their days at Howard University. Duncan, who had already been part of the District Government, had been an acquaintance of Dugas, but only a passing acquaintance of Washington's. In time the circle grew, to include aides Joseph Yeldell, Comer Coppie, Ben Gilbert, Sam Eastman and others. But Washington's was essentially a one-on-one style of decision-making, supported by a hot line, and it persisted except in crisis situations.

For their retreats, the Washington inner circle choose public places - all within walking distance of the District Building - Kostin's, O'Donnell's, the Hotel Washington, and, occasionally, the dining room of the Washington Technical Institute. In times of controversy and tension, such as the conflict of interest charges against inner-circle member Yeldell, then director of the Department of Human Resources, the circle met in private homes.

Among the Barry insiders, opinions vary on who makes up the inner circle. Here are a few nominations: "Del Lewis, Ivanhoe Donaldson, John Wilson, Polly Shackleton, and on particular problems, say the arts, maybe Peggy Cooper," says Max Berry, who advises on local party politics and financial matters. Del Lewis argues, "I'm not sure a Kitchen Cabinet exists and I'm not sure I'm in it, but we still maintain close communications." Yet it was with the Lewises that the Barrys managed an out-of-town weekend.

Another indication of the people closest to Barry is who he can reach with a fast press of the telephone button. Direct lines exist to Donaldson; Elijah Rogers, city admistrator; Judy Rogers, corporation counsel; Dwight Cropp, city government executive secretary; Al Russo, head of the DHR; Florence Tate, his press secretary, James Gibson, economic development aide, Arrington Dixon, chairman of the D.C. City Council, and Robert Moore, housing director, as well as the fire, police and command centers. What hasn't developed yet is a social arbiter, a Dave Powers, who can serve the nonpolitical roles of social host, bon vivant, court jester.

"I'm professionally gregarious; but after working 18 hours a day, often attending social functions as part of the job. I want some solitude. I watch television," says Barry.

But in the meetings of the inner circle, Barry is arbitrator, instigator and listener. During the recent teachers' strike, according to one insider, Donaldson, Cropp, Reid and Elijah Rogers would trash out strategy. Ideas would be offered and the group would chew them over. In these meetings, Reid was always the reticent one, offering a comment, but not dominating. When a conclusion was needed, then Reid offered the solution. He had the last word.

Basically, for those who have watched Barry's career from civil rights activist to the city's top official, there are few surprises in the inner circle. Donaldson was part of the organization meeting of the Student Nonviolent Coordinating Committee that elected Barry its first president. The closeness and respect between the two men is reflected in the way Barry waits for Donaldson to speak at meetings and how Donaldson has been permitted to bring his own base of people into the administration.

His confidence in Reid also dates from that time. "Since the first time Marion got arrested in Washington, we have worked very closely," says the 62-year-old Reid. 'I guess its's a son-teacher relationship. I enjoy seeing someone develop and the one thing that's always been very exciting about Marion is that he's interesting. We share a tremendous enthusiasm that life can get better."

In the heady public protest days of Barry's early Washington career, he met Thornell Page and Jim Palmer. Page, then head of Friendship House, a Southeast community organization, was involved in areas similar to the youth employment projects of Barry's organization, Pride. Palmer, a law enforcement officer, was often on the opposite side from Barry during demonstrations. Barry frequently found it necessary to vouch for Palmer's credibility with the protestors, building a bond between the two men. "We had distinct differences at first," says Palmer. "He got me to understand what the movement meant. I think I passed along that this is a city of many lifestyles and you have to learn to live with them all.

Through each political campaign and job, the circle grew. Audrey Rowe walked into Barry's office at the school board one day in 1972, asking for his help on the Children's March for Survival. "I was a little anxious, after all, I was going in to meet the great Marion Barry, the activist and organizer. I walked out feeling he was terrific, he listened, he asked the right questions," remembers Rowe.

The only time they bitterly clashed was when Rowe heard that Barry was against the nomination of Barbara Sizemore as school superintendent because she was a woman. Rowe fired off an angry telegram, saying sexism in a black male was as deplorable as racism in a white male. She left town for a meeting, Barry tracked her down, and chewed her out for her gullibility. That clash cemented their friendship and Rowe was one of the first called as Barry's mayoral plans shaped up.

"What my friends have in common are my self-interests, not their own. They have their own goals, in sense of their personal lives, and I am concerned about their well-being. But my friends are people who are not trying to advance their own cause through me, people like David Eaton," says Barry.

At this point, Effi Barry, a management consultant who has been married to Marion Barry for one year, is not considered a force in the political inner circle. Her successor as first lady of the city, Bennetta Washington, served as a confidant for Walter Washington, a solidarity extending from the longevity of their marriage and her family's extensive ties in the community.

Yet, judging from the rigors of her schedule, Effi Barry is broadening her own interests in almost every level of city life, particularly the arts. One of the most important lessons of her emergence into the limelight, she says, has been judging friendships. "I haven't been in touch with people who are close friends because I don't want to expose them to the demands of public life. I don't want those who are interested in me invading their privacy," she explains. She is constantly confronted with people who only want use of the Barry name. "I haven't been as selective as I plan to be in the future. I am still finding out who are the people doing substantial things."

What Effi Barry, and all of the mayor's confidants are facing right now is the solicitation drag - "Can you get to Marion to do me a favor." Lilian Sedgwick laughs, an annoyed laugh: "Now I'm in great demand. I could easily go somewhere five times a night. Not only do I have a position but I have access, I am a friend of the mayor, and that's a plus, plus. While treat it lightly, I understand the dynamics. So I handle it by making lunches I can get something out of."

Jim Palmer's solution is to listen but not talk. "People are constantly bothering me. They want favors and I tend not to tell him because I figure he has enough worries." Palmer hits on a critical element of the political friendship, thoughtful loyalty. "I give Marion honesty, candidness and constructive criticism. I wouldn't tell him what he wants to hear, I tell him exactly what someone is saying," Palmer says.

Another key, especially for the political friendship, is the lack of the even exchange syndrome. Barry knows that when Dovey Roundtree, the attorney and minister, is having her regular lunch at O'Donnell's, he can join her and not have to bargain. "My greatest value to him is my faith in him," says Roundtree. Barry calls her and Whitlock his Washington mothers.

In the end, the repeated test of a political friendship, is the understanding of the friend's absence. Lorraine Whitlock used to open her door and find Barry standing there, ready to talk. "That hasn't happened since the election, but that doesn't change our respect and concern," says Whitlock. David Eaton, who says his friendship with Barry is stronger since their political differences in the campaign, says he and the mayor call each other frequently, "and we are always missing one another. But he will call after a night meeting and say, 'Can I have a few minutes?' "

That's the value of the inner cirlce, they are reliable and have no misgivings about their friendship when the telephone isn't ringing.

Or when they are left waiting at the table at the Hotel Washington. CAPTION: Pictures 1, 2, and 3, Three of the mayor's counselors are from left, Ivanhoe Donaldson, Herbert Reid and Lilian Adkins Sedgwick; Illustration, no caption, by Hal Hoover - The Washington Post; Picture 4, Max Berry, By Ken Fell - The Washington Post; Picture 5, Rev. David Eaton by Charles Del Vecchio - The Washington Post; Picture 6, Jim Palmer By Harry Naltchayan - The Washington Post; Picture 7, Dave Abrahamson By Joe Helberger - The Washington Post