Abstract. Let H(B) denote the space of all holomorphic functions on the unit ball B of + n . Let ϕ = (ϕ 1 , . . . , ϕ n ) be a holomorphic self-map of B and g ∈ H(B) with g(0) = 0. In this paper we study the boundedness and compactness of the generalized composition operatordt t from generalized weighted Bergman spaces into Bloch type spaces.