A hollow fiber membrane separation device with two flow spaces, of which a first space is formed by the capillary tube passages of a hollow-fiber bundle cast at its ends into a sealing compound, and a second space is formed by a housing enclosing the fiber bundle. The first space is sealed off by caps, placed on the sealing compounds, with seals running over the peripheral areas of the sealing compounds. The housing, into which the hollow-fiber bundle is drawn, at each end of its casing has tooth-like or pinnacle-like projections formed by axial notches or indentations running out freely. The tooth-like or pinnacle-like projections have extensions extending from the sides of the projections and extending to the adjacent tooth-like or pinnacle-like projection.