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A new kind of tangent derivative,M-derivative,for set-valued function is introduced with help of a modified Dubovitskij-Miljutin cone.Several generalized pseudoconvex set-valued functions are introduced.When both the objective function and constraint function are M-derivative,under the assumption of near cone-subconvexlikeness,by applying properties of the set of strictly efficient points and a separation theorem for convex sets,Fritz John and Kuhn-Tucker necessary optimality conditions are obtained for a point pair to be a strictly efficient element of set-valued optimization problem.Under the assumption of generalized pseudoconvexity,a Kuhn-Tucker sufficient optimality condition is obtained for a point pair to be a strictly efficient element of set-valued optimization problem.