No progress was reported yesterday in either of the two strikes currently affecting the Washington music scene.

Representatives of the National Symphony musicians and management met in offices of the Federal Mediation Service. At the same time, in other rooms, Sam Jack Kaufman president of Musicians Union Local 161-710, and Martin Feinstein, executive director of the Kennedy Center, were carrying on negotiations in the strike by members of the orchestra that plays for performances in the Kennedy Center Opera House.

When the latter session was over, both men agreed there had been no movement toward ending that strike, now in its third day.

Following the symphony negotiations, Austin Kiplinger, president of the National Symphony Association, who is not a member of the negotiating team but sat in on yesterday's meeting, said, "Things are still hanging fire. We are in contact and all on call." Describing the session as "calm in mood and spirit," he said. "We have made adjustments and there has been a spirit of give and take."

William Foster, chairman of the players' negotiating committee, said, "There has been progress in that we have had a face-to-face meeting. We have not yet reached an agreement but we are on call from the mediator."

Meanwhile, the musicians in both strikes are continuing their picketing outside the Kennedy Center.