A dual clutch transmission has a housing, a drive shaft arrangement, an output shaft and a countershaft. A plurality of gear sets is supported on the drive shaft arrangement and the countershaft, respectively. The gear sets are shifted by means of respective shifting clutches in order to engage different gears. The countershaft is connected to the output shaft via a constant output gear set. The gear sets are divided between two gear trains. A first forward gear and a reverse gear are each assigned to a different gear train. The gear set for the reverse gear is driven via an auxiliary shaft, which is in turn driven via a specific gear set. The specific gear set is assigned to the same gear train as the reverse gear.