After the inauguration yesterday, amid a throng of onlookers, they took one ballot, and no one got a majority. Then councilor Walter Sullivan stood up and said, "I move we adjourn until next Monday." It may not be the last time.

One year, it took more than 600 ballots for the Cambridge City Countil to choose a mayor; no one expects it to be that bad this year, but few observers are predicting it will be quicker either.

When voting resumes Monday night, unless a deal has been cut, the voting will likely resemble yesterday's tally--the four liberals banded together in support of one of their number, and the five conservative Independent councilors unable to decide which among them will get the post.

Councilors Alfred E. Vellucci and Leonard J. Russell are without question the two top contenders for the spot. Both are Independents, though Vellucci traditionally acts as the swing vote on the nine-member council, joining with the liberal Cambridge Civic Association (CCA) bloc to support the city's controversial rent control program.

Russell probably has the support of the other three Independents; after serving a term as vice-mayor, he is in line for the mayoralty by the tradition of rotating the top post among the councilors. But without Vellucci or one of the liberals he cannot be elected.

Vellucci, though, badly wants to be mayor--he declared his candidacy even before the vote count was finished in the November election, and he has since broken with the CCA on some housing votes to the delight of the Independents.

Meanwhile, the CCA four are left out in the cold, because, according to sources, the Independents have been unwilling to negotiate with them.

Housing is certainly the biggest bone of contention in the bargaining. For their part, the Independents are likely to be trying to persuade Vellucci that his liberal stand on housing issues did not help him in last fall's election, where he received the fewest votes of the nine winners.

If they can get him to switch his stand on rent control, or, more likely, obtain his pledge to allow the city's anti-condo legislation to be watered down, Vellucci may win their votes for mayor.

Meanwhile, the CCA councilors would probably love to get Vellucci alone and try to wrestle a few promises from him. Support for their liberal housing policies would probably win him their four votes and the mayor's chair. Without commitments from Vellucci, the CCA bloc will almost certainly not back him.

But Vellucci is also walking a thin line--falling out of favor with the Independent bloc might hurt his re-election chances in 1983. He might decide his safest alternative is to back Russell if it appears he can't get the votes himself.

One factor in the Independent discussions may be William J. Walsh, a local attorney and Cambridge's leading proponent of condominium conversion. Walsh was an important force in the Independent campaign last year.

All the pieces are in place, in other words, for a stalemate that could last for weeks or months and dozens of ballots. But surprises are not uncommon in the mayor's race--Thomas W. Danehy was not expected to win the chair four years ago, and many were surprised at the speed of the victory in 1980 of Francis H. Duehay '55.

The position of mayor doesn't really accord with all the fuss--largely a ceremonial post, the office carries with it the duty to chair city council meetings and sit on the school committee. The school board seat is less important this year than some others, because the Independents already hold a 4-2 edge on the board.