In this paper a novel procedure is developed for evolutionary cross power spectra (ECPS) estimation of bivariate nonstationary stochastic processes. Specifically, the ECPS is determined by estimating the statistical moments of energy-like response quantities of lightly damped linear filters excited by nonstationary stochastic processes. In this context, a smoothing procedure is incorporated by using the Savitzky-Golay (S-G) moving average filter to obtain reliable ECPS based even from a limited number of available records. Further, a refinement of the approach is proposed relying on polynomial based functions of the system output. Several numerical examples, including nonstationary processes with known spectra, and historic accelerograms are used to assess the reliability and accuracy of the proposed procedure.