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We introduce and study a new system of variational inclusions with (H,η)-accretive operators, which contains variational inequalities, variational inclusions, systems of variational inequalities, and systems of variational inclusions in the literature as special cases. By using the resolvent technique for the (H,η)-accretive operators, we prove the existence and uniqueness of solution and the convergence of a new multistep iterative algorithm for this system of variational inclusions in real q-uniformly smooth Banach spaces. The results in this paper unify, extend, and improve some known results in the literature.