The invention relates to an apparatus and a process for mass- and/or energy-transfer between two media, in particular between blood and a gas/gas mixture, having a chamber (1) through which a first medium, in particular blood, flows and in which a bundle of mass- and/or energy-permeable hollow fibers through which the second medium can flow and around which the first medium can flow is arranged transverse to the flow direction of the first medium, in which the chamber (1) is configured as an elastic shell (3) at least in a region which completely surrounds the bundle, where a rigid housing (6) is arranged around the elastic shell (3) and the inner wall of the housing contacts the shell (3) in a plurality of first regions (9) and the inner wall of the housing is not in contact with and is in particular at a spacing from the shell (3) in at least one second region (10), preferably a plurality of second regions (10) in the direction of the extension of the hollow fibers, where the one hollow space or at least one of the plurality of hollow spaces formed in the second regions (10) between shell (3) and housing (6) joins a fluid connection (11) passing through the wall of the housing.
