In this paper the notion of the zero-divisor Cayley graph G (Z n , D 0 ) , where (Z n , ⊕, ) is the ring of residue classes modulo n, n ≥ 1, an integer and D 0 is the set of nonzero zero-divisors, is introduced and it is shown that G (Z n , D 0 ) can be decomposed into components, if n is a power of a single prime and it is connected, if n is a product of more than one prime power.