  We discuss compact four-dimensional Z_N x Z_M type IIB orientifolds. We take
a systematic approach to classify the possible models and construct them
explicitely. The supersymmetric orientifolds of this type have already been
constructed some time ago. We find that there exist several consistent
orientifolds for each of the discrete groups Z_2 x Z_2, Z_2 x Z_4, Z_4 x Z_4,
Z_2 x Z_6, Z_2 x Z_6' and Z_6 x Z_6 if anti-D5-branes are introduced.
Supersymmetry is broken by the open strings ending on antibranes. The rank of
the gauge group is reduced by a factor two if the underlying orbifold space has
discrete torsion.
