A method for flushing a fuel cell system during a power-down cycle includes conveying air by an air conveying device through a cathode space of a fuel cell and releasing the conveyed air through an exhaust air line. An outlet valve is cyclically closed and opened during the power-down cycle, where an opening duration depends on an amount of air that is conveyed and the outlet valve connects an anode discharge line to the exhaust air line. The conveyed air is guided from a delivery side of the air conveying device directly to the exhaust air line at least in part through a system bypass.