In this paper, we introduce iterative methods for finding a common element of the set of solutions of a system of equilibrium problems, the set of fixed points for an infinite family of nonexpansive mappings and a family of strictly pseudocontractive mappings, and the set of solutions of the variational inequalities for a family of $\alpha$-inverse-strongly monotone mappings in a Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our proposed schemes. The strong convergence results are obtained via the (CQ) method.
