Time‐average statistics of the response of the bilinear hysteretic system to an excitation with approximately white‐power spectral density and approximately Gaussian probability distribution are determined, using electronic‐analog techniques. Results are presented for the mean‐squared amplitude, the power spectral density, and the probability distribution of the response. The applicability of the Krylov‐Bogoliubov method of equivalent linearization to this problem is investigated by comparing predicted and experimentally measured values of the mean‐squared level of response.