An axle drive for a motor vehicle, comprising an electric machine coupled by a rotor shaft to a transmission for the axle drive, wherein a torque can be transferred from the electric machine to an intermediate shaft with a first gear stage and from the intermediate shaft to another gear train, in particular a differential, with a second gear stage, wherein the rotor shaft or a shaft segment coupled to the rotor shaft is supported in a bearing element, wherein a fluid supply is designed to convey a liquid, in particular oil, into an intermediate space between the bearing element and a side shaft on the axle drive through a fluid channel, and from the intermediate space into the rotor chamber in the electric machine.