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.