The invention relates to a two-stage fuel cell air supply system with pure high-speed dynamic compressors, which bring particularly favourable installation space requirements for a vehicle application. In the majority of cases dynamic compressors of radial type are used. The low pressure compressor is driven by a high speed electric motor, which supplies the necessary electrical energy to the system, also supplying the high pressure stage, connected to a turbine as a free-wheeling unit which leads to a certain energy recovery from the originally supplied electrical energy. In addition to the intermediate cooling of both compressor stages, the adjustable blow-by device as a by-pass for the fuel cell has a particular role in guaranteeing the stability of the operation of the entire air supply system and prevention of pumping damage to the compressor at all operating points of the fuel cell.