On the basis of the concept of semismothness* a new Newton-type method is derived which is applicable to the numerical solution of generalized equations (GEs). If the right-hand side of the considered GE is strongly metrically regular around the solution, then  the Newton step may easily be performed on the basis of the limiting coderivative of the cosidered multifunction. This method is applied to a GE which governs Nash equilibria in presence of nonsmooth terms in the objectives of the single players.This is a joint research with H. Gfrerer (Linz).