The Kennedy Center and the Metropolitan Opera yesterday, announced plans to cooperate in presenting some of the world's leading ballet companies in both houses as well as on tour.

Rodger L. Stevens, chairman of the center; Anthony A. Bliss, executive director of the Metropolitan, and Martin Feinstein, executive director of the Center, explained that the new cooperative management will make it possible for such companies as the Stuttgart Ballet and the Royal Ballet of London to come to this country for longer tours than they have made in the past.

The Stuttgart for instance, the first company that will tour under the new arrangement, will appear in Washington, New York, Philadelphia, New Jersey's Garden State Arts Center, and Chicago for a total of eight weeks from mid-May to mid-July. On its last tour it played only in Washington and New York.

Bliss, speaking for the Met, recalled that the late impresario, Sol Hurok, used to tell the Met:

"Any weeks you have vacant in your house, I will take." Since Hurok's death, Bliss said, no managers have come around with offers like that, "and we have to keep our house full. We cannot afford an empty house."

Feinstein said that negotiations for a visit by the Royal Ballet were under way now whereas, prior to the new arrangement, economic problems caused by inflation had made future tours by the Royal Ballet doubtful.

Stevens called attention to a directive in the Kennedy Center's charter from Congress shall both present productions "and take them to other cities." All three men agreed that the costs of touring opera areso great that the new cooperative management does not at present contemplate any operatic activity.