The resignation Friday of Robert L. Green as the University of the District of Columbia's third president has left a leadership vacuum that already has triggered skirmishing among factions at the university over the selection of Green's replacement.

The 15-member board of trustees, which faces the difficult task of picking UDC's fourth president in eight years, also must resolve a host of problems emerging from the damaging controversy over Green's expenditures of university funds for personal trips and consultants.

The trustees, who for weeks were divided over whether to stand by Green or seek his ouster, are now grappling with who should become the new board chairman -- an appointment that could have a tremendous impact during a fragile transitional period. Among those under serious consideration are trustees N. Joyce Payne; Herbert O. Reid Sr., who is legal counsel to Mayor Marion Barry; Donald A. Brown; Peter B. Edelman and Thomas A. Hart.

The choice of a new board leader, likely to occur next month when the incumbent, Ronald H. Brown, steps down, will have extraordinary political implications. Most importantly, it will determine the amount of political autonomy the university will enjoy from the District government and the extent of Barry's control over the board. Many agree that the election of Reid as chairman would signal that the board was moving closer to Barry's sphere of influence.

Barry publicly remained aloof from the three-month-old controversy until last week, when he criticized the board for lax financial oversight and urged it to act quickly to resolve the crisis engulfing Green. Now he appears poised to play a more aggressive role in the conduct of the university, much as he did with the District's Lottery Board and Board of Elections after he became dissatisfied with their operations.

A new board chairman also must shoulder responsibility for shaping the trustees' response to continuing audits of university finances and the recently launched investigations by the FBI and the U.S. attorney's office.

All these factors have combined to create a sense of urgency among rival factions at UDC, who see an opportunity to promote radical changes within the university leadership.

"This is a dangerous period, because in a period where there is weak leadership or leadership that is not supported across the board, the crazies are going to come out of the woodwork and that can tear the place apart," said one top UDC official who declined to be identified.

Green, 51, who was unavailable for comment yesterday, resigned under pressure Friday after a five-hour emergency meeting of the trustees. He signed an agreement with the board that entitles him to his $74,900-a-year salary and health and retirement benefits for one year. Green and his family will be allowed to remain in the university president's residence in Northwest Washington for 90 days.

Jostling between factions began when it became clear that Green would be ousted, and intensified immediately following the board's announcement that Claude A. Ford, a UDC vice president, had been appointed as Green's interim replacement.

Faculty and alumni leaders criticized the board for picking Ford without consulting other members of the university community and demanded to be included in the selection of a permanent president.

"The board should consult with the different constituencies of the university, especially the faculty, in a systematic way," said George Zachariah, president of the Faculty Association. " . . . The university will not have a good future until the university de-politicizes the presidency."

Green's resignation also could influence the status of top administrators who were appointed by Green, including vice president and provost Maxie C. Jackson, budget director W. Louis Stone, vice president Dwight Cropp, and spokesmen Chester Higgins and Gilbert A. Maddox. The university's eight deans last week asked that Jackson, Stone and Cropp be placed on administrative leave.

The possibility of openings at the highest levels of the university administration already has started a scramble for promotions, according to some university officials.

Trustees interviewed after the emergency session Friday said Ford would remain as interim president for no more than 60 days. During that period, the board will select an acting president who will serve for one year, while the trustees conduct a national search for a permanent president, trustees said.

Several trustees said they hope to recruit a retired university president or professor to step in as acting president.

Trustee Edelman said the board was eager to find someone "who could come in for a year or two and be above the fray and help restore some stability on the campus and lower the temperature level."

University sources have mentioned several potential candidates for acting president, including Albert Manley, a retired president of Spelman College in Atlanta who now lives in the District, and Paul T. Cooke, former president of D.C. Teachers' College.

Some UDC officials have urged the board to choose as a permanent replacement for Green a Washingtonian who is familiar with the District's byzantine political system. Sources say that during the past few weeks, when Green's tenure became increasingly shaky, several names surfaced, including those of D.C. Board of Education Chairman R. David Hall; school board member David Eaton (At Large); Vincent Reed, a Washington Post vice president and a former D.C. school superintendent, and UDC vice president Cropp.

Cropp's future is unclear, however, because he is perceived by many as being close to the mayor. Cropp, a former aide to Barry, is well liked by many staff members at UDC. But he became embroiled in the Green controversy after The Washington Post reported recently that, while secretary to the District of Columbia, Cropp gave a consulting contract to a longtime Green associate just before Cropp was named a UDC vice president. While serving as D.C. secretary, Cropp also hired the wife of UDC board chairman Ronald H. Brown and Denise Elarms, a niece of Green's wife, Lettie.

"Dwight is muddied, but not dirty," said one top UDC official.

Several trustees have conceded that finding a satisfactory successor to Green and persuading that person to take the job may be difficult, in view of the troubled eight-year history of the publicly financed university, with 1,365 faculty and staff and about 15,000 students.

"I think the history, and not just the current controversy, does add to the problem," Edelman said. "I don't think there is any doubt about that. On the other hand, the challenge is quite important. A lot of people in higher education really want UDC to succeed. So I think there may be some people out there who will regard it as so important that that counterbalances the difficulty."

Selecting a new board chairman will be equally difficult.

By a one-vote margin, the board last month nominated Herbert Reid to replace Brown, whose term expired a year ago but who agreed to stay on until the mayor appointed someone else to fill his seat on the board. Usually the board's nomination would assure Reid's selection. But his close ties to the mayor, particularly at the height of the Green controversy, have caused some trustees to question his independence.

"If he even gets near that seat he is going to have problems," said one trustee who opposes Reid.

Reid could not be reached yesterday for comment.

Until recently, Reid's most likely opponent was trustee Payne, who is executive director of a national higher education organization. Several weeks ago, Payne had the support of at least five board members. But Payne's outspokenness has rankled some trustees, and last week she was criticized by Barry at a news conference for airing her complaints about Green outside the confines of the trustees' board room. Some trustees grumbled that the mayor was merely trying to promote Reid's candidacy with his comment.

"I think what the public would see is [that] Herb Reid is the newest member," said trustee Joseph Webb, who was the first board member publicly to call for Green to step aside. "Why should he be chair of the board? Because the mayor sent him to be chair."

According to board sources, trustees Donald A. Brown and Edelman are viewed by some as potential consensus candidates who could unify the board. However, both men are white and some trustees have said it is important to have a black as board chairman of a predominantly black university.

Brown, whose call early last week for Green to be placed on administrative leave was a turning point in the controversy, appears to have the broadest base of support. But some trustees said that it is not likely that Brown, a lawyer and real estate developer, will accept the chairmanship because he is an adjunct professor at the Harvard Business School and would not have enough time to lead the board.

Trustee Thomas Hart has been mentioned as a possible compromise.

The protracted controversy over Green put the board under a spotlight. With 11 of 15 trustees appointed by the mayor, some have criticized the board for being too parochial or narrow, and for allowing many of the problems to fester that ultimately led to Green's resignation.

A few trustees have complained privately that Brown, the current chairman, too often acted independently of other board members. For example, several trustees said they were never shown a copy of Green's five-year contract with the university, even after Green's expenditures came under scrutiny.

Despite conflicts among the board members in recent months, they demonstrated unusual harmony in reaching agreement Friday on Green's resignation, which some trustees said bodes well for the future.

"I think the board acted in a serious, conscientious and intelligent way," said trustee Donald Brown.