Abstract: A non-linear MDOF Duffing system is converted into a time-dependent linear system using the equivalent linearization technique (ELT). The pseudo excitation method (PEM) is adopted to calculate the non-stationary responses of the time-dependent linear system. The method has been shown to be simple, reliable and highly efficient. It is observed that the PSDs of the evolutionary random excitations are not limited to white noise or filtered white noise, and phase lags may exist between excitations.The results of this combined method agree well with the results from Monte-Carlo simulation.