This talk is about a new algorithm for the solution of Generalized Nash Equilibrium Problems (GNEPs). The result of the combination of a potential reduction algorithm and a LP-Newton method, is a hybrid method that has robust global convergence properties and a local quadratic convergence rate. The basis for the proof of the local convergence property is a local error bound condition for the KKT system of a GNEP. Since the application of standard error bound results is difficult, due to the peculiar structure of KKT systems arising from GNEPs, a new sufficient condition is provided. This condition does neither imply local uniqueness of the solution nor strict complementarity. The numerical behavior of the new algorithm is promising.