Fuel cell system and method for operating

Fuel cell system comprises a fuel cell unit (1) with an anode (2) and a cathode (3); a media feeding path for the anode; a media feeding path for the cathode; and a cathode waste gas flow path (4). A compressor (5) for supplying air to the cathode is arranged in the feed path of the cathode. A catalytic burner (8) is arranged in the cathode waste gas flow path. The anode waste gas flow path opens into the burner and/or upstream of the burner in the cathode gas flow path. The combined catalytically converted fuel cell waste gas stream is fed into an expansion machine (7). An Independent claim is also included for a process for operating a fuel cell system. Preferred Features: The expansion machine is a waste gas turbocharger or turbogenerator. The compressor is coupled to the expansion machine via a common shaft.