Chicago teachers overwhelmingly voted last night to strike the nation's third-largest school system, then returned to negotiations, while Philadelphia teachers and the city reached an agreement early today, possibly averting a walkout there.

In three Michigan school districts, strikes that kept 36,000 students out of class last week continued, as did strikes affecting 5,600 students in two western Pennsylvania school districts.

The Chicago Teachers Union, which represents 28,000 professionals, most of them teachers, voted 3,548 to 494 to strike for the third consecutive year, beginning today.

The first day of class for 430,000 students is scheduled for Wednesday.

Board spokesman Bob Saigh said the board would repeat its offer of a 3.5 percent raise, which the teachers rejected early Sunday, when negotiations broke off. The union is seeking a 9 percent increase.

The Philadelphia Federation of Teachers scheduled a ratification vote for this morning after reaching a tentative agreement in negotiations that began Sunday between the city and the union representing 19,000 educators.

"If they ratify, we'll be back no later than 12 noon ," said Marvin E. Schuman, president of the teachers' federation.

The teachers, whose contract expired early Sunday, had said they would go on strike today if no pact were reached. The district's 197,000 pupils are scheduled to start school Thursday.