PhD thesis deals with debris flow hazard assessment on torrential fans. Its main focus is on the known problems pointed out with the already performed research, such as is the way of preliminary classification of torrential catchments to determine those, which are prone to trigger debris flows, furthermore, how to estimate magnitudes of potential debris flows triggered in these torrential catchments, and finally, open questions with regard to debris-flow mathematical modeling on torrential fans, especially their rheological characteristics to be used in mathematical models and how topography influences modelling results. In the first part, we focus on geomorphological parameters of torrential catchments and various methods for classification of torrential catchments prone to debris-flow triggering. Based on analysis of the selected methods, a new classification method was proposed for classification of debris-flow prone catchments, transitional catchments and catchments with no debris- flow hazard. This new method was then tested in selected torrential catchments in Slovenia. For debris-flow magnitude assessment, we applied the LS-Rapid triggering model. With its application in the Bela torrential catchment (NW Slovenia), we could identify several active landslides and potentially unstable areas, which could under unfavorable conditions turn into active landslides and trigger debris flows. A detailed study and debris-flow modeling was then carried out on the Stože landslide (NW Slovenia), which was triggered in November 2000. For debris-flow model parameters, which cannot be determined with sufficient reliability without analyzing soil samples in detail in a geomechanical laboratory, we proposed an estimation of their limit values, which can be used for potential landslide modeling. Soil samples were taken from the Stože landslide source area for testing in a geomechanical laboratory. In this way, rheological properties of a potential debris flow could be determined, and then used in debris-flow mathematical routing model on a torrential fan. Based on our own laboratory study, and additionally testing of the Flo-2D model, we proposed instructions how to assess potential debris-flow rheological characteristics. Furthermore, with the Flo-2D model we tested the influence of different topographical datasets on debris-flow modeling results. We applied different publicly available topographical data and commercial LiDAR data to develop DEM with different resolutions. The debris-flow modeling results, obtained by using new public available LiDAR based data and the Flo-2D model, turned out to be very /plausible. Finally, we comprise single steps described in previous sections into a new methodology for debris-flow hazard assessment on torrential fans, culminating in the debris-flow hazard mapping. The PhD thesis ends up with some recommendations for further research in this field.