Summary: This paper continues a line of investigation in part I [N. Argaç, E. Albaş, Sib. Mat. Zh. 43, No. 6, 1211-1221 (2002); translation in Sib. Math. J. 43, No. 6, 977-984 (2002; Zbl 1016.16023)]. Let \(A\) be a \(K\)-algebra and \(M\) an \(A/K\)-bimodule. N. Hamaguchi [in Sci. Math. Jpn. 54, No. 2, 337-342 (2001; Zbl 1004.16034)] gave a necessary and sufficient condition for \(\text{gDer}(A,M)\) to be isomorphic to \(\text{BDer}(A,M)\). The main aim of this paper is to establish similar relationships for generalized \((\sigma,\tau)\)-derivations.