- Abstract We show that the system of biocrust and vegetation on sand dunes modeled by two coupled ordinary nonlinear differential equations exhibits self-sustained oscillations. Such oscillations can occur on vegetated linear dunes that are mostly covered by biocrust. The vegetation–biocrust interaction underlies these oscillations and these do not occur if only vegetation dynamics is considered. The oscillations are “relaxation oscillations” which are characterized by two alternating attraction processes to equilibrium states with high low vegetation covers. The complex dynamics of the biocrust–vegetation model leads to unexpected scenarios, such as vegetation rehabilitation induced by drought or by grazing during which the system shifts to one of the bistable state dominated by a higher vegetation cover, or rehabilitation of vegetation that is induced by decrease in precipitation. The oscillation periods range from decades to millennia and they can interact and be affected by the climate system variability.