In this note, we introduce abelian modules as a generalization of abelian rings. Let R be an arbitrary ring with identity. A module M is called abelian if, for any m is an element of M and any a is an element of R, any idempotent e is an element of R, mae = mea. We prove that every reduced module, every symmetric module, every semicommutative module and every Armendariz module is abelian. For an abelian ring R, we show that the module M-R is abelian iff M[x](R[x]) is abelian. We produce an example to show that M[x, alpha] need not be abelian for an abelian module M and an endomorphism alpha of the ring R. We also prove that if the module M is abelian, then M is p.p.-module iff M[x] is p.p.-module, M is Baer module iff M[x] is Baer module, M is p.q.-Baer module iff M[x] is p.q.-Baer module.