Abstract: Device for the transfer of material and/or heat from one medium stream to another medium stream is assembled from interconnected modules, each module having a number of hollow membrane fibres or tubes, which fibres or tubes are designed to be flowed through by a first medium, while a second medium can flow outside the fibres of tubes, and the ends of the fibres of tubes projecting a sealed manner through module walls lying essentially opposite each other and open into chambers with orifices for the supply and discharge of the medium, the supply orifice and the discharge orifice of adjacent modules being in register and being connected to each other in a fluid-tight manner.