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Debris flows are often described as a succession of surges, which are characterized by enhanced peak depth and velocity and therefore by a tremendous increase of their destructive power. For given characteristics of the base flow, if the channel is sufficiently long to allow an appreciable wave development, the linear stability analysis in shallow streams is shown to provide a reasonable prediction of the critical flow condition and of the instability growth rate. The one‐dimensional (1‐D) theory, however, does not allow the determination of the wave period of the fastest growing perturbations. Debris waves most frequently develop following a mechanism similar to water roll waves: Instabilities grow up becoming clearly distinguishable waves, and then waves overtake one another with increasing wave period and amplitude. The typical hydrograph of a multiple‐peak event is shown to be composed of a first surge …