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We compute the form of the Lagrangian of N=1 supersymmetric theories withgauged axion symmetries. It turns out that there appear generalizedChern-Simons terms that were not considered in previous superspace formulationsof general N=1 theories. Such gaugings appear in supergravities arising fromflux compactifications of superstrings, as well as from Scherk-Schwarzgeneralized dimensional reduction in M-theory. We also present the dualsuperspace formulation where axion chiral multiplets are dualized into linearmultiplets.Comment: References added and few misprints correcte

Axion gauge symmetries and generalized Chern-Simons terms inN=1 supersymmetric theories