An exchanger device for transferring mass and/or energy between a first medium and a second medium includes a chamber having a first inlet and first outlet of the first medium and through which the first medium can flow. The chamber is equipped with at least one, preferably a plurality, of one mass- and/or energy-permeable exchanger hollow fibers connected at one end to a second inlet and at the other end to a second outlet of the second medium. The second medium can flow through the fiber(s) and the first medium can flow around the fiber(s). The chamber is equipped with at least one pump element for displacing the first medium in and out of the chamber in a pulsing manner. The pump element has an elastically deformable element, is connected to a third inlet of a third medium used as a driving medium, and is expandable by the third medium.