The invention relates to a fuel cell system including a first heat exchanger via which cathode feed air can be supplied to a fuel cell or fuel cell stack and to which a mixture of afterburner exhaust gas of an afterburner and cathode exhaust air having materialized in the fuel cell or fuel cell stack can be supplied for heat exchange between the cathode feed air and the mixture via the first heat exchanger. In accordance with the invention it is provided for that a second heat exchanger is provided via which the cathode feed air can be supplied from the first heat exchanger to the fuel cell or fuel cell stack and via which the afterburner exhaust gas can be supplied to the first heat exchanger to form the mixture, in thus achieving a heat exchange between the afterburner exhaust gas and the cathode feed air.