NOVELTY - The system (1) has a first duct element (19) connecting an exhaust air outlet of a cathode chamber (5) of a fuel cell (3) with an exhaust air inlet of an intercooler (13). A second duct element (21) connects an exhaust air outlet of the intercooler with an exhaust air inlet of a humidifier (14). Supply air and exhaust air pass through the intercooler and the humidifier. A third duct element (23) indirectly connects an exhaust air outlet of the humidifier with environment. Valve devices (20, 22, 24) selectively adjust the duct elements as a flow path for the exhaust air from the chamber.    USE - Fuel cell system for producing electrical drive power in a fuel cell vehicle (claimed) e.g. passenger car and commercial vehicle. Can also be used for a driverless transport system, logistic vehicle, watercraft and aircraft.    ADVANTAGE - The valve devices selectively adjust the duct elements as the flow path for the exhaust air from the cathode chamber, thus providing the warm exhaust air in the humidifier in start situations of the system, and hence reducing risk of condensation of water and ice formation in a region of the humidifier and/or the cathode chamber. The system avoids blockage of gas-guiding sections in the humidifier and/or the cathode chamber, and reduces pressure loss in an operating situation. The system improves an efficiency of the humidifier by a high temperature, and obtains a long service life of a proton exchange membranes in the fuel cell. The system ensures simple, efficient, quick and reliable start with a high efficiency of gas humidification, and increases acceptance of the system by a user. The system is efficiently and reliable operated.    DETAILED DESCRIPTION - The valve devices are 3/2 directional valves. The humidifier is a membrane humidifier. The fuel cell is a proton exchange membrane fuel cell. An INDEPENDENT CLAIM is also included for a method for operating a fuel cell system.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of a fuel cell system in an operating mode.    Fuel cell system (1)    Fuel cell (3)    Cathode chamber (5)    Intercooler (13)    Membrane humidifier (14)    First duct element (19, 21, 23)    Valve devices (20, 22, 24)