In this paper, we describe H-differentials of some well known NCP functions and their merit functions. We show how, under appropriate conditions on an H-differential of f, minimizing a merit function corresponding to f leads to a solution of the nonlinear complementarity problem. Our results give a unified treatment of such results for C¹-functions, semismooth-functions, and for locally Lipschitzian functions. Illustrations are given to show the usefulness of our results.