We study a D=4, N=1, type IIA orientifold with an orbifold group ZN and ZN×ZM. We calculate the one-loop vacuum amplitudes for the Klein bottle, cylinder, and Möbius strip and extract the tadpole divergences. We find that the tadpole cancellation conditions thus obtained are satisfied by the Z4, Z8, Z'8, Z'12 orientifolds while there is no solution for Z3, Z7, Z6, Z'6, Z12. The Z4×Z4 type IIA orientifold is also constructed by introducing four different configurations of 6-branes. We argue about perturbative versus nonperturbative orientifold vacua under T duality between the type IIA and the type IIB ZN orientifolds in four dimensions.