We have proposed in [7], a new projection or extragradient method to solve many variational inequalities problem classes. The corresponding algorithm is established under continuity and pseudomonotonicity of the underlining mapping. The numerical implementation results express its remarkable efficiency. In this paper, we extend the application of this algorithm to the class of nonlinear constraints. The main idea is to linearize the constraints in the neighbourhood of each iterate, then we calculate the necessary projections. It is important to point out that most of the theoretical results already obtained in our previous work will be modified and justified according to the class of problems studied in this paper. The global convergence is proven under weak hypothesis. The numerical results are very encouraging and show that the method is also very efficient to solve this class of problems.
