For the drainage basin of the gauging station Pegelstation Vernagtbach (2640 m a.s.l., 11.44km^2; Oetztal Alps, Austria) which is 84% glacierized by the Vernagtferner, combined discharge and meteorological data are available since 1974. For this catchment a discharge model was developed which takes into account the meteorological and hydrological factors involved in the formation and distribution of runoff in a highly glaciated basin as a system of four parallel linear reservoirs which correspond to three different parts of the glacier, and a small groundwater reservoir. The model input is the meltwater produced at the glacier surface and calculated with an energy balance model based on global radiation, longwave radiation, air temperature, relative humidity, wind velocity, and albedo. In addition, input may be caused by liquid precipitation. The paper presents the results for the period 1978-1985. The discharge model yields hourly mean values of the runoff, which agree well with the measured runoff data.