2010 Mathematics Subject Classification: Primary 05C25. Secondary 20K01, 05C45. Let Cay(G;S) denote the Cayley graph on a finite group G with connection set S. We extend two results about the existence of cycles in Cay(G;S) from cyclic groups to arbitrary finite Abelian groups when S is a “natural” set of generators for G. This research was supported in part by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada.