In recent years, the focus of research about natural hazards has turned from single-hazard studies to multi-hazard ones. While single hazards (like earthquakes, floods, droughts, etc.) have been extensively studied in the past and many quantitative statements about intensities and severities are available, quantitative studies about multi-hazards and dependencies are still rare. This paper introduces new statistical models for the dependencies of cat-event processes of different hazard types based on Poisson-type event processes. Moreover, the models are applied to data for several natural hazard events from the Danube area in Europe. The analysis should help to bridge the gap between the more conceptual contributions to this discussion by providing empirical evidence on interactions on a large-scale region.