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It is shown that the known conditions of wave interaction do not cover all possibilities for effective wave interaction. New, more general conditions for such interaction are identified in this article. The new conditions contain the known conditions as a special case. The simplest cases of «three-wave» interaction are considered as examples. In these examples, one of the interacting waves is a given wave. The most important and interesting case is when two waves with different frequencies can interact with a stationary periodic structure. The conditions for experimental observation of the new conditions are described.