<p>Upslope (anabatic) winds during the day and downslope (katabatic) winds during the night are common features of boundary layers in mountainous terrain during clear and calm weather conditions. A milestone in the theory of slope flows is the Prandtl solution of the viscous/diffusive equations of motion and thermal energy for the flow of a stably stratified fluid over a uniformly heated planar slope of infinite extent. The model was originally developed for the steady state. In this study we consider the class of unsteady Prandtl-like flows arising from an abrupt change of slope buoyancy from one value (possibly zero) to another. This sudden change is an idealization of rapidly changing thermal conditions on real slopes, such as occurs around sunrise/sunset or when the sun appears/disappears from behind a cloud deck. The solution of the unsteady Prandtl model equations is used to estimate the times for the wind and buoyancy fields to attain specified percentages of their final steady-state values. The response times are calculated as functions of height, Prandtl number, and slope angle. The analysis is exact for a Prandtl number of 1, and approximate for Prandtl numbers near 1. The response times can provide a basis for establishing, for a given case, whether a quasi-steady state is even physically realizable within the daytime or nighttime phase of the diurnal cycle.</p>