The present invention relates to a method for shutting down a generator unit (1) comprising a fuel cell device (100) having the steps (a) shutdown of a current generation via a control unit (510); (b) detection of at least one anode temperature of an anode (122) of the fuel cell device (100), in particular during a cool-down process; (c) blocking of an escape of carbon monoxide from an anode chamber (120) in which the anode (122) is arranged at least partially, in particular, at least for the most part, completely, if the anode temperature is higher than the first limit temperature T1; (d) at least partial removal of carbon monoxide from an anode chamber (120) in which the anode (122) is arranged at least in part, in particular, at least for the most part, completely, if the anode temperature falls below a first limit temperature T1. The present invention further relates to a generator unit (1), a vehicle having this generator unit (1) and a use of this generator unit (1).