In this study the potential increase of extreme precipitation in a future warmer European climate has been examined. Output from the regional climate model (RCM) HIRHAM4 covering Europe has been analysed for two periods, a control period 1961-1990 and a scenario 2071-2100, the latter following the IPCC scenario A2. The model has a resolution of about 12 km, which is unique compared with existing RCM studies that typically operate at 25-50 km scale, and make the results relevant to hydrological phenomena occurring at the spatial scale of the infrastructure designed to drain off rainfall in large urban areas. Extreme events with one- and 24-hour duration were extracted using the Partial Duration Series approach, a Generalized Pareto Distribution was fitted to the data and T-year events for return periods from 2 to 100 years were calculated for the control and scenario period in model cells across Europe. The analysis shows that there will be an increase of the intensity of extreme events generally in Europe; Scandinavia will experience the highest increase and southern Europe the lowest. A 20 year 1-hour precipitation event will for example become a 4 year event in Sweden and a 10 year event in Spain. Intensities for short durations and high return periods will increase the most, which implies that European urban drainage systems will be challenged in the future.