An exploratory study is done to modelling of rivers on volcano slopes. Beside the occurrence of mud flows or lahars these rivers are characterised by unsteady supercritical flow and large suspended-sediment concentrations. A fully coupled 1D model is presented for the rivers, provided that lahars do not occur. It can simulate unsteady supercritical flow (Froude numbers between about 1 and 1.8) with volumetric sediment concentrations less than about 10%. The redistribution of the suspended-sediment concentration (i.e., the lag between concentration and transport capacity due to sediment relaxation) causes instabilities of the bed conformable to antidunes. Calculations with a numerical model using Preissmann's implicit scheme, and applied to a river on the Kelud Volcano in Indonesia, show the rapidity of bed-level variations and the upstream propagation and growth of bed disturbances. These results offer a deeper understanding in the problems of the rivers on the Kelud. Furthermore it yields a base for investigating the efficacy of sabo works.