District of Columbia School Board President David H. Eaton and Vice President Nathaniel Bush won reelection to their posts yesterday with no opposition, marking the first time in eight years that the board's top leadership has remained intact for more than one term.

Eaton, who first won the president's job in January with a narrow, 6-t0-5 majority, was reelected yesterday by a vote of eight yes and one abstention with two members absent. Bush received eight yes votes, one no, and one abstention. One member was absent.

"Basically, our unity is very good. Some people on the board are going to give us difficulty, but that just helps us keep alert," said Eaton after the vote that made him the first board president since 1977 to win successive terms, and marked the first time since 1974 that both the president and vice president were reelected.

Board member R. Calvin Lockridge (Ward 8) was the only abstention in the presidential vote and board members Barbara Lett Simmons (At-Large) and Bettie Benjamin (Ward Five) were absent. Simmons abstained and board member John Warren (Ward Six) voted no in the balloting for vice president.

" Former Chicago Mayor Richard Daley said, 'When you've got the votes in your pocket, you do what you want.' Why should somebody get embarrassed?" said Lockridge in explaining why Eaton faced no challengers.

After the vote, Eaton said his priorities in 1983 would be to "maintain the level of the 1983 school budget."

He said he would "like to receive the mayor's understanding" on recent transition team recommendations to expand D.C. Mayor Marion Barry's role in education, "which are not all that we would like them to be."

Board members said before the balloting that strong support for Eaton represented a desire for continuity in what could be a turbulent year.

"We have the problem of dealing with leasing empty school space this coming year. Then there is the mayor's grab for power in getting education under his belt. These are good reasons for continuity," said board member Wanda Washburn (Ward 3).

"I think the board president ought to have a two-year term anyway. One year barely gives you enough time to get your knees under the table, and Eaton has done a good job," she said.

In past years the school board was often at odds with city officials on matters ranging from autonomy to the budget. Eaton's election last January, when he defeated board member Eugene Kinlow, signalled the emergence of a board with closer ties to Barry and furthered the isolation of the remaining board members who had been in office during the school system's bitter 1979 teachers strike.

Among the members voting for Eaton and Bush yesterday was Frank Smith (Ward One), who must leave his seat by Jan. 2 to assume the Ward One City Council seat, to which he was elected last fall. He was able to vote in yesterday's election because the meeting was scheduled for a time before his resignation took effect.

As president, Eaton had the right to call the organizational meeting any time after the board's last regular meeting of the year. In the last three years, the organizational session has been held in January.

Simmons was critical of the timing of yesterday's meeting. "He has the meeting early, and that does not let the new member participate in this selection process," she said. No successor for Smith has yet been chosen.