A response approximation method for stochastically excited, nonlinear, dynamic systems is presented. Herein, the output of the nonlinear system isapproximated by a finite-order Volterra series. The original nonlinear system is replaced by a bilinear system in order to determine the kernels of this series. The parameters of the bilinear system are determined by minimizing, in a statistical sense,the difference between the original system and the bilinear system. Application to a piecewise linear modelof a beam with a nonlinear one-sided supportillustrates the effectiveness of this approach in approximatingtruly nonlinear, stochastic response phenomena in both the statistical momentsand the power spectral density of the response of this system in case ofa white noise excitation.