Abstarct: In this thesis, we investigate necessary and sufficient conditions for the existence of a m- cycle system in complete graphs k_n for n odd, and also k_n-I for n even, where I is 1-factor. Moreover , we prove necessary and sufficient conditions for the existence of a 6-cycle system of k_n-E(F),where F is any spanning forest that all vertices in F have odd degree. An m-cycle system of G will be formally described as an ordered pa.ir (V,B),where V is the vertex set of G and B is the set of m-cycles.