A moisture exchange module includes a bundle of moisture-permeable hollow fiber membranes through which a first gas stream can flow. The bundle of hollow fiber membranes is arranged in a housing, the housing being provided with line elements for supplying and discharging a second gas stream, which flows around the hollow fiber membranes. Between the bundle of hollow fiber membranes and the housing there is at least one flow space, which extends over at least approximately the entire length of that region of the bundle of hollow fiber membranes through which the first gas stream can flow. The at least one flow space surrounds only a small part of the circumference of the bundle of hollow fiber membranes, so that ultimately a moisture exchange operated in cross-current mode is formed. This can preferably be used for the humidification of feed air for fuel cell systems.