NOVELTY - The system (1) has an afterburner (25) which is provided for burning fuel contained in anode exhaust gas using cathode exhaust gas as oxidants. An anode exhaust gas guide (26) is provided for guiding the anode exhaust gas to afterburner, and cathode exhaust gas guide (23) is provided for guiding cathode gas to afterburner. A bypass guide (27) is connected with cathode exhaust gas guide downstream of fuel cell (2) and upstream of afterburner, through which cathode exhaust gas is conductible. A conveyor device (28) is provided downstream of fuel cell for conveying cathode exhaust gas.    USE - Fuel cell system for motor car.    ADVANTAGE - The fuel cell system allows delivery of cathode exhaust gas to the afterburner independent from the cathode gas stream, in maintenance-free manner. The cathode exhaust gas stream can be divided so that the supply of cathode exhaust gas to the afterburner is adjustable independent of the fuel cell. The pressure or the mass flow through the afterburner or bypass guide is set as accurately as possible. The promoted flux at cathode exhaust gas is no longer exclusively adjustable by the cathode gas source or conveyor device. The interference in the fuel cell running electrochemical reactions can be avoided. The wear can be reduced, and the service intervals are extended so that the operation of fuel cell system is made inexpensive. The conveyor device downstream of fuel cell with burner designs can be realized at a higher pressure demand, since the pressure of the afterburner is adjustable. The amount of air or the amount of cathode exhaust gas in the afterburner can be selectively adjusted by conveyor, while the need of the afterburner can be optimally adjusted. The fuel cell system can operate energy-efficiently. By positioning conveyor device in the bypass guide, very precise adjustment of the cathode exhaust stream, and favorable and precise injection of the cathode exhaust gas in bypass line or in the afterburner can be realized. The combustion or conversion of fuel in the anode exhaust gas can be achieved effectively and efficiently. The pollutants in anode exhaust gas can be removed reliably.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for method for operating fuel cell system.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the fuel cell system.    Fuel cell system (1)    Fuel cell (2)    Cathode exhaust gas guide (23)    Afterburner (25)    Anode exhaust gas guide (26)    Bypass guide (27)    Conveyor device (28)