Let R be a *-- prime ring with involution * and F be a nonzero (α, β)--derivation associated with a (α, β) -derivation d commuting with *. We prove classical results of Posner and Herstein for Lie ideals of rings with involution. Also, we discuss the commutativity of *-prime rings addmitting a generalized (α, β)-- derivations F satisfying several conditions on Lie ideals.