  Compact Type IIB D=4, N=1 orientifolds have certain U(1) sigma model
symmetries at the level of the effective Lagrangian. These symmetries are
generically anomalous. We study the particular case of $Z_N$ orientifolds and
find that these anomalies may be cancelled by a generalized Green-Schwarz
mechanism. This mechanism works by the exchange of twisted RR-fields associated
to the orbifold singularities and it requires the mixing between twisted and
untwisted moduli of the orbifold. As a consequence, the Fayet-Iliopoulos terms
which are present for the gauged anomalous U(1)'s of the models get an
additional untwisted modulus dependent piece at the tree level.
