We study the impact of the recently introduced underspread/overspread classificationon the spectra of processes with square-integrable covariance functions. We briefly review the most prominent definitions of a time-varying power spectrum and point out their limited applicability for {\em general} nonstationary processes. The time-frequency-parametrized approximation of the nonstationary Wiener filter provides an excellent example for the main conclusion: It is the class of underspread processeswhere a time--varying power spectrum can be used in the same manner as the time--invariant power spectrum of stationary processes.