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In this paper, we introduce and study a new system of general nonconvex variational inclusions involving four different nonlinear operators (SGNVI) and prove the equivalence between the SGNVI and a fixed point problem. By using this equivalent formulation, we establish the existence and uniqueness theorem for solution of the SGNVI. We use the foregoing equivalent alternative formulation and two nearly uniformly Lipschitzian mappings S 1 and S 2 to suggest and analyze some new two-stepdoi:10.1186/1029-242x-2013-377 fatcat:dntix5zuvraf3aq4a5h2oiqiwy