This paper presents some new results in the theory of Newton type methods for variational inequalities and their application to nonlinear programming. A condition of semi-stability is shown to ensure the quadratic convergence of Newton's method and the superlinear convergence of some quasi-Newton algorithms, provided the sequence defined by the algorithm exists and converges. A partial extension of these results to nonsmooth function is given. The second part of the paper considers some particular variationnal inequalities with unknowns {x, l) generalizing optimality systems. Here only the question of superlinear convergence of {xk} is considered. Some necessary or sufficient conditions are given. Applied to some quasi-Newton algorithms they allow to obtain the superlinear convergence of {xk}. The application of the previous results to nonlinear programming allows to strenghten the know results, the main point being a characterization of the superlinear convergence of {xk} assuming a weak second-order condition without strict complementary.