NOVELTY - The fuel cell system comprises a fuel cell (12), a gas generating system (14) for providing reformate gas from a hydrocarbon-containing fuel, and an afterburner (18) arranged in an exhaust gas line (42) downstream of the fuel cell, where a part of the exhaust gas of the fuel cell passes through the afterburner and combustible constituents of the exhaust gas are thermally reacted in the afterburner. Exhaust gas recirculation (20) is provided downstream of the afterburner toward the inlet side of the gas generating system.    USE - Used as a fuel cell system.    ADVANTAGE - The fuel cell system is simple and has good reliability.    DETAILED DESCRIPTION - The fuel cell system comprises a fuel cell (12), a gas generating system (14) for providing reformate gas from a hydrocarbon-containing fuel, and an afterburner (18) arranged in an exhaust gas line (42) downstream of the fuel cell, where a part of the exhaust gas of the fuel cell passes through the afterburner and combustible constituents of the exhaust gas are thermally reacted in the afterburner. Exhaust gas recirculation (20) is provided downstream of the afterburner toward the inlet side of the gas generating system such that the part of the exhaust gas is fed into the reactant stream of the gas generating system. The fuel cell system is designed such that the entire water required during the operation of the fuel cell system is provided in a gaseous form by the operation of the fuel cell system. The water is completely provided in gaseous condition. The exhaust gas recirculation comprises a cooling and/or heating for the exhaust gas. A switchable bypass line is intended for the fuel cell, which is construed so that in a starting phase, the reformate gas is fed from the gas generating system under bypassing the fuel cell to the afterburner. The exhaust gas recirculation comprises a conveyor device for the exhaust gas. The conveyor device is a venturi-nozzle. A recirculation for the cathode exhaust air is provided from the cathode to the inlet side of the gas generating system. A heater is arranged into the recirculation for the cathode exhaust air. An INDEPENDENT CLAIM is included for a method for operating a fuel cell system.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic representation of a fuel cell system.    Fuel system (12)    Gas generating system (14)    Afterburner (18)    Exhaust gas recirculation (20)    Exhaust gas line. (42)