- The aim of this project is to consider and study a new iterative scheme for solving the general nonconvex variational inequalities. We plan to prove the convergence criteria for the suggested iterative methods under suitable conditions. In the first year, we will study and discuss some important basic results and consider some new theorems about the general iterative scheme for general nonconvex variational inequalities in the normed spaces. In the second year, we will focus our study to the heart of our project, that is, we will suggest and analyze the iterative scheme for finding the approximation solvability of the system of general nonconvex variational inequalities in the normed spaces. In conclusion, we point out that the results of this project are the extension and improvements of the earlier and recent results in this field. Much work is needed to develop this interesting subject.