In this paper, we introduce and consider a new class of variational inequalities involving two operators, which is called the general nonconvex quasi variational inequality. Several special cases are discussed. We use the projection technique to establish the equivalence between the general noncon vex quasi variational inequalities and the xed point problems. This alternative equivalent formulation is used to study the existence of a solution of the general nonconvex quasi variational inequalities. Using these equivalent for-mulations, we suggest and analyze a wide class of new extragradient methods for solving the general nonconvex quasi variational inequalities. Convergence criteria of these new iterative methods is considered under some suitable conditions.