Let R be a * -prime ring with characteristic not 2, σ, τ : R → R be two automorphisms, U be a nonzero * -(σ, τ ) -Lie ideal of R such that τ commutes with * , and a, b be in R.

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In this paper, it is defined that left *-α-derivation, generalized left *-α-derivation and *-α-derivation, generalized *-α-derivation of a *-ring where α is a homomorphism. The results which proved for generalized left *-derivation of R in [1] are extended by using generalized left *-α-derivation. The commutativity of a *-ring with generalized left *-α-derivation is investigated and some results are given for generalized *-α-derivation.

Let R be a prime * -ring where * be an involution of R, α be an automorphism of R, T be a nonzero left α- * -centralizer on R and d be a nonzero * -α-derivation on R. The aim of this paper is to prove the commutativity of a * -ring R with the followings conditions: i) if T is a homomorphism (or an anti-