Mayor Edward J. Sullivan will face one of his toughest battles in his campaign for reelection, as the city's traditionally drawn-out majoralty race gets under way this morning. Five of the nine elected councilors have announced their candidacy for the chief magistrate's posts.

Weighing against Sullivan this year will be the tradition that no Cambridge mayor should serve two terms. Though he polled a heavy plurality of the city last November, Sullivan has only one pledged supporter, old-timer John D. Lynch, in the Council.

Another likely candidate for mayor is Councilor Thomas McNamara, who has received the pledge of Al Vellucci's vote on the first ballot. In the 1956 elections, McNamara abstained for two weeks before casting the fifth and deciding ballot for Sullivan.

The minority of four Cambridge Civic Association councilors may benefit from the disagreement among the Independents and succeed in electing one of their number. If they have their way, they will probably elect the city's first woman mayor, Mrs. Pearl K. Wise or Mrs. Cornelia Wheeler.

Former mayor Joseph A. DeGuglielmo '29, a C.C.A. councilor, who has made himself unpopular by his consistent opposition to Vellucci and other council members, has promised to vote for any C.C.A. candidate.

Councilor Charles A. Watson, who also tossed his hat in the ring, admitted last night that he had only one vote so far, his own. It is conceivable, though, that the C.C.A. bloc would switch its votes to Watson, rather than allow Sullivan's reelection.