The authors discuss a homogenization problem for general two-dimensional nonlinear composites. Nonperiodic distributions of inclusions is supposed to be statistically homogeneous. The authors prove convergence of the solutions of the corresponding boundary value problems when a small parameter \(\varepsilon\) tends to zero in the Sobolev space to the solution of the homogenized problem. Similar problems were discussed independently by J. J. Telega [“Stochastic homogenization: convexity and nonconvexity”, in: Nonlinear homogenization and its applications to composites, polycrystals and smart materials. Dordrecht: Kluwer, 305–346 (2004)].