Acoustic pressure fields measured by an observer when the source or observer or both are moving is a nonstationary random process even if the source generates a random process which is stationary in the reference frame of the source. The causes of nonstationarity are classified as being due to wave expansion, directivity, and Doppler shift. This paper is concerned with developing two-dimensional (frequency–time) spectral descriptions for the processes by constraining the processes to fit within the framework of the ‘‘evolutionary spectral density.’’ Earlier literature has described how evolutionary spectra may be estimated from single sample realizations. Spectral representation forms for free-field acoustic processes produced by moving monopole and dipole excitations are derived from the fundamental wave equations.