An electric axle drive unit for an axle of a vehicle has an electric machine. The drive output of electric machine can be connected to the input of a transmission device. The electric drive unit has a differential gear, the input member of which is connected to an output of the transmission device. The output members of the differential gear can be connected respectively to a left-hand and a right-hand driveshaft of the axle. At least one transmission stage of the transmission device and the differential gear are arranged on opposite sides of the electric machine in the axial direction. The differential gear is connected to the transmission stage by means of a hollow shaft.