Abstract: An apparatus for effecting mass and/or heat transfer, comprising a bundle of hollow filaments of substantially equal length, the ends of which are embedded in a sealing compound, a substantially cylindrical housing with connecting branches for the supply and removal of at least two media, the first medium being guided through the hollow filaments and the second medium being guided radially inwardly at the flow inlet of the housing and radially outwardly at the flow outlet, the housing comprising a substantially tubular body and two caps. The connecting branches are disposed in the caps. Each cap forms with the ends of the substantially tubular body two distributor chambers, the first of which is disposed on the end face and the second on the outside jacket of the tubular body. The outside jacket of the tubular body has at least one port in the area of the second distributor chamber. The interior of the substantially tubular body may widen conically from one end area to the other.