The objective of this paper is to consider new generalized systems of nonlinear mixed variational inequalities including 3k-distinct nonlinear relaxed cocoercive operators. We proposed k-steps explicit iterative methods including projection operators for this considered system and present the
equivalent fixed point problem of this new generalized systems of variational
inequalities. This equivalent fixed point problem suggest to us k-steps explicit
iterative algorithms to obtain an approximate solution of the considered system. Convergence results of k-step explicit iterative algorithms are obtained.