Let R be a prime ring and I a nonzero ideal of R. Let $alpha,; u,; au;R{ ightarrow}R$ be the endomorphisms and $eta,;mu;R{ ightarrow}R$ the automorphisms. If R admits a generalized $(alpha,;eta)-derivation$ g associated with a nonzero $(alpha,;eta)-derivation;delta$ such that $g([mu(x),y]);=;[ u/(x),y]alpha,; au$ for all x, y ${in}I$, then R is commutative.