During monitoring of an electromotively driven fuel pump of a fuel feed unit for a motor vehicle, a pump current is monitored as a function of a pump voltage or of a pump rotational speed. Through a comparison of the pump current with the pump voltage or the pump rotational speed, it is detected whether leakage or dry running of the fuel pump is present. The fuel feed unit does not require any pressure sensor for this purpose, and is therefore of particularly simple construction.