The general actions of matter-coupled supergravity have Peccei–Quinn terms that may violate gauge and supersymmetry invariance. In addition, 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 supergravity and exhibit conditions that have to be satisfied for their mutual consistency. This extension of the previously known 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.