The non-Gaussian response distribution of a single degree-of-freedom system with nonsymmetric nonlinearities subjected to nonwhite random excitation with nonrational spectra is investigated. The nonstationary and stationary probability densities of stochastic responses are calculated by employing the method which consists of the non-Gaussian equivalent linearization technique and the use of the moment equations approach. The non-Gaussian probability density function for the response distribution is expressed in terms of the potential of the system and employed for determining the equivalent linear coefficients. The results are compared with the corresponding digital simulation results.