NOVELTY - The device comprises a process gas flow system (322) for conducting a process gas to be humidified, and a moist gas flow system (323) for passing a moist gas. A water vapor-permeable element (321) is comprised such that the gases are separated from each other to form a water vapor passage. The flow systems are formed in a downstream portion (329) such that the gases are guided in co-current flow with respect to a flow direction of the process gas, and in an upstream portion (328) of a moistening device in a position deviating from the co-current flow guide.    USE - Humidifying device for humidifying process gas in polymer electrolyte membranes (PEM) fuel cell of fuel cell assembly for driving vehicle (all claimed) e.g. motor vehicle.    ADVANTAGE - The system complexity in humidification of process gas is reduced, and a current electrical load independent of an operating point of the fuel cell is guaranteed. The efficiency of the water vapor transfer of all possible flow guides is reduced. The passive boundary of moisture transmission is achieved by the co-current flow of the gas streams in the downstream portion of the humidifying device. Therefore, space-saving humidification of process gas is achieved. The excessive humidification of process gas is prevented without enlarging a necessary space. The need for a bypass line and a bypass valve to the humidifying device is omitted. The improvement of the flow guide is achieved. The moistening is independent of the volumetric flow rates of the gas streams in the humidifying and independent of a current operating point of the fuel cell. The damage of the humidifying device is avoided.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a fuel cell assembly.    DESCRIPTION OF DRAWING(S) - The drawing shows a longitudinal cross-sectional view of the humidifying device.    Water vapor-permeable element (321)    Process gas flow system (322)    Moist gas flow system (323)    Upstream portion (328)    Downstream portion (329)