It is known that along any watercourse a clear relation exists between the sediment grain-size and the corresponding bottom slope in certain reaches. At the basin scale, if we neglect the localized deviations due to geological constraints, this corresponds to the usual concave profile and progressive sediment fining in the downstream direction. Although this configuration is, perforce, not in equilibrium, yet it usually exhibits a quasi-stationary behaviour at very long (historical and even geological) time-scale. The 0-D, two-reaches, two-grain-size hydro-morphological model presented in this paper, based on a number of reasonable and verified simplifications, gives reason of the extremely slow evolution of most rivers and provides a quantitative approach for evaluating their “response time”. Differently from previous formulations, the response time appears here to be affected, among others, by the granulometry of the sediment input. Applications of the model to schematic rivers of different sizes and configurations are here reported and discussed.