We study a D=4, N=1, type IIA orientifold with an orbifold group Z(N) and Z
(N)XZ(M). We calculate the one-loop vacuum amplitudes for the Klein bottle,
cylinder, and Mobius strip and extract the tadpole divergences. We find th
at the tadpole cancellation conditions thus obtained are satisfied by the Z
(4), Z(8), Z(8)', Z(12)' orientifolds while there is no solution for Z(3),
Z(7), Z(6) Z(6)', Z(12). The Z(4)XZ(4) type IIA orientifold is also constru
cted by introducing four different configurations of 6-branes. We argue abo
ut perturbative versus nonperturbative orientifold vacua under T duality be
tween the type IIA and the type IIB Z(N) orientifolds in four dimensions. [
S0556-2821(99)03624-3].