This paper first addresses the problem of conditionally simulating stationary, space-time, Gaussian random fields. A method developed for quadrant-symmetric, stationary, space-time fields is extended to account for the imaginary part of the complex cross-spectrum. The case of amplitude- and frequency-modulated (AFM) nonstationary space-time fields is studied next. The evolutionary spectral density and cross-correlation structure of such a class of nonstationary random fields are analyzed in terms of the envelope and frequency modulation functions. A method for the conditional simulation of AFM space-time fields is advanced. The AFM nonstationary fields are mapped to a domain where the conditional simulation is performed as for stationary, space-time fields. Examples are given to illustrate the use and capabilities of the method including applications to the simulation of earthquake ground motions.