As has long been recognized in teleseismic studies, smooth rupture propagation significantly modifies the azimuthal variation in elastic wave radiation and introduces a dependence of peak motion on the ratio of rupture velocity to wave propagation velocity. Rupture propagation also has a first-order effect on the ground motions close to faults as calculated from models of coherent rupture. For engineering purposes, it is important to know whether the effect occurs only with coherent ruptures, or whether it is a more general phenomena of propagating faults. This question was examined by both analytical and Monte Carlo studies of models of nonuniform ruptures. The principal models were defined by ruptures moving continuously in time along the fault with random variations in rupture velocity or in slip amplitude. These models were richer in high frequencies than the corresponding smooth ruptures. The randomness introduced a new corner into the spectrum at a frequency that is simply related to the coherence length of the random variations and to the azimuth between the fault and station. The lower frequency corner due to the overall rupture was preserved. For the model with varying rupture velocity the azimuthal variation in spectral amplitude was enhanced over that for the smooth rupture. For the model with varying slip the azimuthal variation was the same as for a smooth rupture. These models showed directivity effects as strong or stronger than the corresponding smooth rupture, providing that the average rupture velocity was the same. Monte Carlo simulations with statistical models gave peak amplitudes with the same general dependence on rupture velocity as the peak amplitudes from smooth ruptures although in the mean the peak motions were enhanced in the incoherent model. An analytic expression was also derived for the mean spectrum of an extreme model in which rupture occurred in little patches distributed with complete randomness over the fault surface and in time. Even this model showed some effects of directivity. The results of our study are consistent with the interpretation that rupture propagation produces destructive interference in the radiated motion; incoherence reduces this interference and in general leads to higher peak motions and spectral levels.