The Kennedy Center has reached a basis for agreements with four of its employes' unions, averting a strike that could have sabotaged the opening of the Christmas ballet season and next Sunday's Kennedy Center Honors program.

The four unions, representing the stagehands, the Opera House orchestra, the box office and wardrobe workers, all had contracts that expired in recent months. At that time, anticipating that the Kennedy Center might be closed by a strike, the management of the National Symphony Orchestra had begun looking for alternate places to play, including Constitution Hall. But NSO spokesmen said this was merely a routine precaution and did not mean that a strike was really imminent.

Two of the unions had set strike deadlines, but had not given up hope for a settlement, according to Jack Ryan, chairman of the stagehands' union, who sat in on negotiations for all four contracts. "The stagehands had a strike permit to begin at 7 a.m. Monday," Ryan said yesterday, "and the musicians had one for Friday." After intensive negotiations going late into Friday evening, the stagehands agreed at noon on Saturday not to strike. "We were still far apart until after Thanksgiving," Ryan said. "Friday and Saturday is when they really started closing the gap. It got down to practically nothing by about 11 p.m. on Friday. The issues left were very minute -- nothing that we would strike about." The final negotiations were with the musicians, who reached substantive agreement a few hours after the stagehands' meeting.

No new contracts have been signed yet, but Ryan said he expects final agreements and signed contracts "within a couple of weeks."

Details of the agreements were not immediately made available, but from general descriptions provided by both sides the settlements appear to maintain approximately the status quo on work rules, with some increases in salaries. The Kennedy Center management had gone into the negotiations with proposals for drastic reductions of personnel requirements both in the stagehands and the orchestra, but apparently modified these demands. "There are no major changes in the work rules," Ryan said. "They have some relief in a few areas where they felt it was needed. Some gray areas have been clarified, and I think there is a respectable increase in wages."

Kennedy Center chairman Roger Stevens, who did not take part in the negotiations, still did not have specific details of the new agreements when he was contacted yesterday, but he seemed content with the settlement. "The unions were very cooperative and tried to see our side and be constructive," he said. "After all, they have problems, too, with the cost of living and everything."

Asked whether he thought the new contracts would affect the price of tickets at the Kennedy Center, Stevens said, "I don't see why. My own feeling is that our prices have gone as high as we can go."