We consider a certain class of unital simple stably finite C^*-algebras which
absorb the Jiang-Su algebra Z tensorially. Under a mild assumption, we show
that the crossed product of a C^*-algebra in this class by a strongly outer
action of Z^N or a finite group is Z-stable. As an application, we also prove
that any strongly outer actions of Z^2 on Z are mutually cocycle conjugate.