A reexamination of the momentum balance in shallow rivers, with scaling appropriate to the Saint Lawrence and the Fraser, shows that frictional forces exceed accelerations over most of the tidal cycle. Consequently, tidal propagation in shallow rivers is more properly envisaged as a diffusion than as a wave propogation phenomenon. The long time lags associated with low waters, unexplainable in terms of a simple wave propagation model, are easily accounted for by an equally simple diffusive model.