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A two-colored digraph (D^{(2)}) is called primitive if there exist nonnegative integers (h) and (k) such that for each ordered pair of vertices (v_a) and (v_b) there are ((h,k))-walk from (v_a) to (v_b) and (v_b) to (v_a). The competition index of a primitive two-colored digraph is the smallest positive integer (h+k) such that for each pair of vertices (v_a) and (v_b) there is a vertex (v_c) such that there are ((h,k))-walks from (v_a) to (v_c) and from (v_b) to (v_c). We study the generalized competition index of two-colored Wielandt digraphs.