On proper holomorphic mappings from domains with T-action

We describe the branch locus of a proper holomorphic mapping between two sm oothly bounded pseudoconvex domains of finite type In C-2 under the assumpt ion that the first domain admits a transversal holomorphic action of the un it circle. As an application we show that any proper holomorphic self-mappi ng of a smoothly bounded pseudoconvex complete circular domain of finite ty pe in C-2 is biholomorphic.