A recent study by Carbone et al. revealed "episodes" of warm-season rainfall over North America characterized as coherently propagating signals often linking multiple mesoscale convective systems over spatial scales of 1000-3000 km and timescales of 1-3 days. The present study examines whether these propagating signals are found in two numerical weather prediction (NWP) models commonly used today, namely, the Eta Model from the National Centers for Environmental Prediction and the newly developed Weather Research and Forecast (WRF) model. The authors find that the diurnal cycle of rainfall over much of the United States east of the Rockies is poorly represented, particularly over the central United States, where a nocturnal rainfall maximum is observed. Associated with this nocturnal maximum is an axis of propagating rainfall emanating from the western High Plains in the late afternoon, extending across the Midwest overnight, and occasionally continuing to the Appalachians on the second day. This propagation is largely unrepresented in NWP models. Only where rainfall maximizes during the late afternoon and remains local do models perform reasonably well. Even in these areas there is a tendency, especially in the Eta Model, for rainfall to occur several hours too early. Using idealized simulations, the authors demonstrate that fundamental propagation errors arise using cumulus parameterizations contained in NWP models. The authors also show that errors in the timing of convection, combined with propagation errors, lead to a poor phase locking of predicted rainfall to diurnal and orographic forcing. This, in turn, degrades the coherence of propagating signals in diurnally averaged rainfall frequency diagrams. The authors suggest that until these "zeroth-order" statistical shortcomings in NWP models are rectified, prospects for accurate short-range, model-based prediction of warm-season rainfall remain poor.