After weeks of increasingly tense relations with management over contract negotiations, the musicians of the Cleveland Orchestra went on strike Monday.

They said the action meant they would not leave Tuesday for a residency at Indiana University — several days of teaching and coaching — that was to be followed by a 10-day visit to Miami, a lucrative annual residency for the orchestra. Some hope of progress remained, though. A negotiation session with a mediator started at noon on Monday.

The players’ contract expired in August, and the musicians announced several weeks ago that Monday was a deadline for progress. Management, citing dire economic conditions at the orchestra and staff salary cuts, has asked the players to take a 5 percent pay cut this year, go back to par next year and accept a 2.5 percent raise the following year. It is also seeking some cuts in benefits. The players offered an immediate freeze in salary this year, arguing that they have already made a series of sacrifices over the past four years.

They also maintain that slipping salaries threaten the orchestra’s status as one of the country’s premier ensembles; management says the Cleveland Orchestra has kept that status despite trailing, in salary terms, other major orchestras like the New York Philharmonic, Boston Symphony, Chicago Symphony and Philadelphia Orchestra.

“We may be considered to be amongst the best in the world musically, but we are a far cry from being compensated that way or treated that way,” the players said in a statement. “In our judgment, if we were to accept management’s offer it would be the beginning of the end of the Cleveland Orchestra as one of the leading ensembles in the world.”

The orchestra management posted a brief statement on the orchestra’s Web site:

“We have every reason to believe that with mediation, good will and good judgment will prevail the bargaining table,” said Gary Hanson, the executive director. “In the event of an extended work stoppage we have plans to reschedule any concerts which could be canceled.”

Trouble also loomed to the west. Players of the Seattle Symphony said on Sunday that they had rejected a management offer and noted that they had authorized a strike, though no work stoppage was expected for the moment.