: Let R be a commutative ring. An R-module M is called a multiplication module if for each submodule N of M, N=IM for some ideal I of R . An R-module M is called a pm-module, i.e., M is pm, if every prime submodule of M is contained in a unique maximal submodule of M. In this paper the following results are obtained. (1) if R is pm, then any multiplication module M is pm. (2) if M finitely multiplication module, then (i) M is pm if and only if Spec(M) is normal if and only if M is a weakly Gelfand module; (ii) M is a Gelfand module if and only if Mod(M) is normal.