  In the paper, a Newton-type method for the solution of generalized equations
(GEs) is derived, where the linearization concerns both the single-valued and
the multi-valued part of the considered GE. The method is based on the new
notion of semismoothness${}^*$ which, together with a suitable regularity
condition, ensure the local superlinear convergence. An implementable version
of the new method is derived for a class of GEs, frequently arising in
optimization and equilibrium models.
