Abstract. An additive mapping F : R → R is called a generalized derivation on R if there exists a derivation d: R → R such that F (xy) = xF (y) + d(x)y holds for all x, y ∈ R. It is called a generalized (α, β)−derivation on R if there exists an (α, β)−derivation d: R → R such that the equation F (xy) = F (x)α(y) + β(x)d(y) holds for all x, y ∈ R. In the present paper, we investigate commutativity of a prime ring R, which satisfies certain differential identities on the left ideals of R. Moreover some results on commutativity of rings with involutions that satisfy certain identities are proved.