An integrated fiber membrane module for air dehydration and air separation includes dehydration and separation units disposed concentrically in a generally cylindrical module. Air flows through the outer dehydration unit, becomes dried, and is then directed, in an opposite direction, through the separation unit. The permeate gas from the separation unit serves as a sweep gas for the dehydration unit. A portion of dried gas produced by the dehydration unit may be used as a sweep gas for the separation unit, and also for the dehydration unit. The module makes it feasible to dry and separate air using a device which occupies relatively little space, and which is therefore especially suited for use in aircraft and in other cramped environments.