The report gives a review on the glacial-hydrological work carried out since 1974 in the project “Runoff within and from glaciers” of Sonderforschungs-bereich 81 of the Technical University Munich with the aim of creating a deterministic discharge model. Since 1974 the runoff of Vernagtferner glacier has been recorded at the gauge station “Pegelstation Vernagtbach” (catchment area 11.44 km2, mean altitude 3,125 m a.s.l., 81% glaciated). The discharge hydrographs for the years 1974-1980 are discussed and characteristic time intervals with characteristic discharge components are pointed out. Using the different discharge patterns exhibited by different parts of the glacier, a spatial classification for the discharge formation is given, and the different hydraulic conditions are described. The mathematical model which is proposed uses four parallel linear reservoirs for which the storage constants were determined by former experiments. For a fortnight period with dry and sunny weather the discharge is calculated with the energy balance on the glacier surface as input data.