Let A be a normed algebra, let σ and τ be two mappings on A and let M be an A-bimodule. A linear mapping L : A ! M is called a generalized Lie (σ; τ)-derivation if L([x; y]) = [L(x); y] σ; τ [L(y); x]σ;τ+σ(x)mτ(y)- σ(y)mτ(x)
for some m ∈ M and all x; y ∈ A, where [x; y]σ;τ is xτ(y) -σ(y)x and [x; y] is the commutator xy yx of elements x; y. If m = 0, then L is Lie (σ;τ)-derivation. In this paper we investigate the generalized Hyers-Ulam-Rassias stability of generalized Lie (σ;τ)-derivations. We also prove that if the center of A is zero, then every “approximate Lie (I; I)-derivation" is indeed a Lie (I; I)-derivation.