  We show that 4D gauge theories with Green-Schwarz anomaly cancellation and
possible generalized Chern-Simons terms admit a formulation that is manifestly
covariant with respect to electric/magnetic duality transformations. This
generalizes previous work on the symplectically covariant formulation of
anomaly-free gauge theories as they typically occur in extended supergravity,
and now also includes general theories with (pseudo-)anomalous gauge
interactions as they may occur in global or local N=1 supersymmetry. This
generalization is achieved by relaxing the linear constraint on the embedding
tensor so as to allow for a symmetric 3-tensor related to electric and/or
magnetic quantum anomalies in these theories. Apart from electric and magnetic
gauge fields, the resulting Lagrangians also feature two-form fields and can
accommodate various unusual duality frames as they often appear, e.g., in
string compactifications with background fluxes.
