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 Î M and any a Î R , any idempotent e Î 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 , α] need not be abelian for an abelian module M and an endomorphism α 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.