Abstract: This paper is devoted to a nonlinear　complementarity problem with nonsmooth data. The  nonlinear　complementarity problem is reformulated as a system of nonsmooth　equations. Then, a Newton method for solving the nonsmooth equations　is proposed. In each iteration of the Newton method, an element of　the B-differential of related functions, not nonlinear　complementarity function, is required. The superlinear convergence　is shown.

Key words: nonlinear complementarity problem, nonsmooth analysis, optimization,  , Newton methods