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The basic idea of this paper is to give the existence theorem and the method of averaging for the system of functional-differential inclusions of the form ⎧$ẋ\left(t\right)\in F(t,x_t,y_t)$ (0) ⎨ ⎩$ẋ\left(t\right)\in G(t,x_t,y_t)$ (1)