Let G be a Group (finite or infinite) and S be a subset of G not containing the identity element 1 of G .Define the Cayley graph of G with respect to S
denoted by Cay(G
S)
as a graph with vertex set G and there is an edge between two vertices x and y iff x -1 y or y -1 x belong to S .In this paper we prove that connected Cayley graphs of abelian groups are edge hamiltonian.