We introduce and study a new system of nonlinear variational-like inclusions involving s - ( G , η ) -maximal monotone operators, strongly monotone operators, η -strongly monotone operators, relaxed monotone operators, cocoercive operators, ( λ , ξ ) -relaxed cocoercive operators, ( ζ , φ , ϱ ) - g -relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique associated with s - ( G , η ) -maximal monotone operators and Banach contraction principle, we demonstrate the existence and uniqueness of solution for the system of nonlinear variational-like inclusions. The results presented in the paper improve and extend some known results in the literature.