A majority of the governing body of the University of the District of Columbia, including its top two officers, will leave the panel in a week, and D.C. Mayor A. Anthony Williams has yet to come up with a list of nominations to replace them.

The Board of Trustees of the city's only public university is legally required to have 15 members but has been operating with 11 since February. Seven panel members whose terms expired in May were allowed to extend their tenures for 180 days, but they must leave the board Nov. 15.

"There will be a gap in governance," said D.C. Council member Kevin P. Chavous (D-Ward 7), who heads the Education Committee, which would vote on the mayor's board nominations before sending them to the full council for approval.

UDC has gone through years of financial and administrative turmoil, and its board has been accused of doing little to solve the problems. Mayor Marion Barry left some seats unfilled for years at a time, though in October 1998 he filled five vacancies before leaving office.

While the full board meets infrequently, much of its work is done through committees, and board members fear that without a quorum, their efforts will be stymied.

Williams (D) said in an interview Tuesday that he was close to submitting a list of nominees but would not say who is on it. Asked why he did not fill the positions earlier, the mayor said he was having difficulty finding nationally known people to serve on the board of such a troubled school.

"It's a Catch-22. We have to find the very best people, people of national stature," Williams said. But such people, he added, are reluctant to agree to join the board until the school's problems have been solved--even though Williams said he needs them to serve to help solve those problems.

Lawyer and former council member Bill Lightfoot said he was contacted by the mayor Wednesday but was not inclined to join the board for personal reasons. The Rev. Willie Wilson, of Union Temple Baptist Church, is another person the mayor is said to be considering for appointment to the board. He did not return a telephone call seeking to confirm that.

Of the 11 current members, eight are considered regular trustees, one is a student representative and two represent the alumni. A quorum of eight is needed to conduct business. Those leaving the panel Nov. 15 are five regular trustees and two alumni trustees. Four people, including the student representative, will remain.

Chavous has scheduled a public hearing on Nov. 29 to discuss any UDC nominations he might receive from the mayor by then. He said the full council could then take a final vote on the nominees at its next meeting, in December.

"It's extremely disappointing that it's taken so long to have these vacancies filled," Chavous said. "We faced the same level of inaction from mayor Barry with respect to the UDC board. . . . All of us have expressed a commitment to the university, and I believe the mayor must demonstrate that commitment by putting some names forward."

Trustees Chairman Michele Hagans and Vice Chairman Carrie Thornhill--both of whom are leaving the board this month--said the trustees are "very concerned" about the situation. Hagans said the mayor's administration is "overwhelmed" with the job of filling vacancies on city boards and commissions.

"They have so many they haven't figured out that this one is critical," Hagans said. "But this one shouldn't have slipped through the cracks, because the university is a critical element to the economic recovery of the District."

Thornhill said people are hesitating to join the board "when they know there is instability."

Sometimes so few members have shown up for UDC board meetings that the sessions have been canceled. In February, a new member, Bell Atlantic-Washington President Marie C. Johns, resigned after news stories reported that she had not attended the two meetings held after her appointment. Her position remains unfilled.

A Williams spokesman said at the time that the new mayor was trying to determine which boards and commissions needed new members and would offer UDC trustee nominees soon.

CAPTION: Council member Kevin P. Chavous, left, has scheduled a hearing on whatever UDC nominations are made. Trustees Chairman Michele Hagans says the city administration is overwhelmed by vacancies. Bill Lightfoot was offered a seat, and the Rev. Willie Wilson reportedly is being considered.