The effective magnetic nonlinear response of a 3-dimensional composite created by periodical arrays of wires and split-ring resonators (SRR) embedded into a nonlinear dielectric,was analyzed theoretically,the general expression of the effective permeability for the composite with the consideration of the effects of mutual interactions among the SRR was derived,and the nonlinear magnetic response with and without the mutual interaction effects was calculated. It could be demonstrated that the nonlinear permeability is obviously different for the two cases even though the expressions of the nonlinear permeability of them are very similar. The results are expected to have referential meaning for the realization and design optimization of nonlinear metamaterials.