A fuel cell system includes at least one fuel cell and at least one air conveyor that conveys a process air flow to the fuel cell. At least one heat exchanger is also provided, through which the process air flow flows after the air conveyor and through which a cooling medium flow flows. A region with catalytically active material is arranged in the flow direction of the process air flow before or in the region of the heat exchanger. In addition a fuel can be fed to the region with the catalytically active material.