When the deadline arrived Tuesday evening, 38 candidates had filed their nomination papers for the Cambridge City Council and the School Committee.

All nine incumbents are running again for the Council, and four incumbent school committeemen--Francis H. Duehay, assistant dean of the Graduate School of Education, Gustave M. Solomons, James F. Fitzgerald, and John A. P. Good--have filed for the School Committee. Of the other two current committeemen, George F. Olesen Jr. is not seeking re-election, and Barbara Ackerman is a Council candidate.

Mrs. Ackerman is one of two women in the 20-candidate race for the Council. The other woman, incumbent Cornelia Wheeler, also happens to be the only Republican in the competition, although she is not running as such. The elections, to be held November 7, are non-partisan.

To have 20 people in the Council race is nothing special, a long-time City Hall official said yesterday. He recalled that in the past, elections have had anywhere from 83 to 16 candidates. "Those were the days it was a thriving organization," he remarked.

In order to ensure a cross-section of groups, the top nine candidates in the voting win positions on the City Council, and the top six join the School Committee. The new City Council then elects the Cambridge mayor and vice-mayor from within its own group. They also select a City Manager, who is subject to Council removal at any time.

Besides the nine incumbents, others who have filed for the Council are Thomas Danehy, James W. Caragianes, Michael J. McCann, Leonard J. Russell, William F. McConnell, Deighton C. Ashby, Manuel Rogers, Ralph W. Ward, Pasquale R. Coppola, Mrs. Ackerman, and former school committeeman Joseph E. Maynard.