A device for sealing a double clutch transmission of a motor vehicle, with a transmission housing, in which are arranged a clutch chamber with clutch oil and a double clutch, a transmission chamber with transmission oil and a double clutch transmission wheel set and two co-axial drive shafts disposed, one inside the other. One drive shaft is an interior central shaft which extends inside the transmission chamber from the end of the second hollow drive shaft. The two drive shafts each have a sealing element to seal the clutch chamber from the transmission chamber. A mounting component is situated inside and fixed to the transmission housing to support two adjacent sealing elements. A first sealing element forms a seal radially on the hollow drive shaft and a second sealing element forms a seal radially on the central drive shaft to provide a reliable seal and offer a simple ventilation and leakage detection.