The effective response of a class of weakly nonlinear conducting composite media is investigated. We combine the previously developed perturbation expansion method for solving electrostatic boundary‐value problems with the well‐known Rayleigh method for treating periodic composite media to compute the effective conductivities. We derive general expressions for the effective nonlinear response functions and show that the results agree with the generalized Landau’s formula at low inclusion concentrations. Numerical calculations are also obtained for a square array of cylindrical inclusions suspended in a host medium in two dimensions. Possible applications and extensions of the method to more complicated problems are discussed. ©1995 American Institute of Physics.