Cohomologies and anomalies in supersymmetric theories

We analyze the anomaly structure of renormalizable supersymmetric models coupled to supergravity using cohomological methods. We study the cohomology corresponding to superdiffeomorphisms, superlocal Lorentz and super-Weyl transformations. We conclude that in four dimensions superdiffeomorphisms and Lorentz transformations are anomaly free for all the models of interest. We determine the super-Weyl anomalies. (orig.)