  The general actions of matter-coupled N=1 supergravity have Peccei-Quinn
terms that may violate gauge and supersymmetry invariance. In addition, N=1
supergravity with vector multiplets may also contain generalized Chern-Simons
terms. These have often been neglected in the literature despite their
importance for gauge and supersymmetry invariance. We clarify the interplay of
Peccei-Quinn terms, generalized Chern-Simons terms and quantum anomalies in the
context of N=1 supergravity and exhibit conditions that have to be satisfied
for their mutual consistency. This extension of the previously known N=1
matter-coupled supergravity actions follows naturally from the embedding of the
gauge group into the group of symplectic duality transformations. Our results
regarding this extension provide the supersymmetric framework for studies of
string compactifications with axionic shift symmetries, generalized
Chern-Simons terms and quantum anomalies.
