A fuel cell system (1) comprises at least one fuel cell (2) and at least one gas generation system (6) in which at least one component requires air during operation. A compression device (11) is provided to supply the oxygen-containing gas, for example air, to the cathode chamber (4) of the fuel cell. At least one branch line (13) also supplies oxygen-containing gas to the gas generation system component(s) that requires air during operation thereof. Exhaust gases from the fuel cell cathode chamber anode chamber are combined downstream of the fuel cell.