The present study analyses the climate change response of Alpine-Mediterranean heavy precipitation events (HPEs), often associated with hazardous flooding. We investigate HPE properties describing their propagation, scale and intensity, by applying a storm tracking algorithm in an ensemble of convection permitting regional climate models (cpRCMs) under the CMIP5-RCP85 forcing scenario. The climate change response of HPE properties we derive by comparing their mean values for periods nearfuture [2040, 2050] and farfuture [2090, 2100] against those of a present-day period historical [1996, 2005]. By the end of the 21st century the model ensemble projects the region’s surface temperatures to increase by 4.0 ∘C. In this warmer climate HPEs are found to propagate farther and faster. They last longer by 5%, their area increases by 15% and their precipitation volume by 35%. Their maximum precipitation rate increases by 13% and an estimate of severity is found increased by 20%. By differentiating specific HPE categories, regions and seasons we find that landfalling and orographically forced HPEs occurring in fall are most intense, heavy and severe. Most importantly we find that these events are also projected to respond most strongly to climate warming, meaning that they will be even more intense, heavy and severe. Consequently in Mediterranean regions the most dramatic changes must be expected, in particular in Southern Italy. But also in regions north of the Alps, where HPEs are generally weaker than to the south, HPEs are found to occur twice as often in wintertime accompanied with an increase in precipitation volume of about 50%. Our analysis also confirms that even though the Mediterranean climate is generally drier by the year 2100, precipitation amounts associated with HPEs are found to increase by 52%. Further HPEs are projected to be 12% more frequent overall, although their occurrence frequency decreases in summer. Eventually we show that the characteristic HPE properties scale with surface warming, meaning that the warmer the local climate is, the more frequent, intense, heavy and severe are HPEs. Notably statistical tests show that the ten-member cpRCM ensemble provides robust climate change responses of all HPE properties investigated. The projected changes of HPE properties infer an increase of flooding risk for communities of the Alpine-Mediterranean area and thus the results presented here may encourage local authorities in adapting their flood protection measurements to climate change.