In this paper, the problems of decomposing the circulant graph C(subscript n)(k) (resp. the circulant digraph C(superscript * subscript n)(k)) into 4- and 8-cycles (resp. 4-and 8-circuits) are investigated. We obtain some sufficient conditions of the decompositions, and give the necessary and sufficient conditions of the 4- cycle decomposition of C(subscript n)(「n/2」-1) and the 4-circuit decomposition of C(superscript * subscript n) (「n/2」-1).