A fuel cell system has at least one fuel cell and a hydrogen generating arrangement for feeding the fuel cell anode with a hydrogen-containing product gas from a conversion reaction of a hydrocarbon starting substance or hydrocarbon derivative with of water fed supplied by way of a water feeding system. Water recovery devices are provided for condensing water out of the process gas supplied by the hydrogen generating arrangement, and/or out of the cathode waste gas carried away from the fuel cell cathode, and returning the condensed-out water into the water feeding system.