a system for supplying an aircraft with inert gas is provided . the system includes at least one fuel cell with an air inlet and an exhaust air outlet as well as a membrane device with an inlet , an outlet and a vapor - permeable membrane . the exhaust air outlet is in fluid communication with the inlet of the membrane device . the membrane device guides a gas from the inlet to the outlet and to give off to the outside through the membrane any water vapor contained therein . this leads to a cost efficient , passive and reliable dehumidifaction of inert exhaus gas for inerting purposes , and a dehumidification device that does not or only marginally increases the weight of the aircraft .