It took the City Council a month, but its members finally came up with a mayor Monday night. He is Walter J. Sullivan, the independent councillor who topped the vote totals in the November 6 council election.

Although the independents control the council by a 5-4 margin, Sullivan was elected by a coalition he formed with new Vice Mayor Leonard J. Russell and the four members of the council's liberal minority.

Until the coalition was finalized during a Sunday night meeting at the home of former Mayor Barbara Ackermann, a liberal councillor, the independent majority had been unable to decide between independents Sullivan and Thomas W. Danehy.

In return for the mayor's office, Sullivan promised to support a move to replace controversial City Manager John H. Corcoran with James Leo Sullivan, now city manager of Lowell. James Sullivan, who served as Cambridge city manager from 1968 to 1970, is no relation to the mayor.

The mayor also appoints chairmen of council subcommittees, and Mayor Sullivan is likely to favor his new backers for assignments.

Left out of the deal are Danehy and his two independent supporters, Daniel J. Clinton and Alfred E. Vellucci. Danehy called the coalition "a political deal," vowing that he would "lead the fight" to retain Corcoran, who may choose not to resign, and ask for a public hearing on his dismissal.

Mayor Sullivan, who plans to run for Middlesex county sheriff, termed his new post "a definite asset" for the race. "Vellucci and Danehy are still my close friends," he said. "But they must realize I act as an independent politician."