  We compute the form of the Lagrangian of N=1 supersymmetric theories with
gauged axion symmetries. It turns out that there appear generalized
Chern-Simons terms that were not considered in previous superspace formulations
of general N=1 theories. Such gaugings appear in supergravities arising from
flux compactifications of superstrings, as well as from Scherk-Schwarz
generalized dimensional reduction in M-theory. We also present the dual
superspace formulation where axion chiral multiplets are dualized into linear
multiplets.
