An apparatus for the reeling up of fiber bundles, in particular of hollow fiber membrane bundles, and in particular for the manufacture of dialysis filters, includes a reel carrier rotatable around a main axis. The apparatus includes at least two reels which are rotatably supported on the reel carrier, with the axes of rotation of the reels being perpendicular to the main axis of the reel carrier. The apparatus can be used for the wrapping of a fiber bundle with a film, having a receiver of first and second side elements and a flexible channel fastened between them for the reception of the film and the fiber bundle. A drive is provided to move at least the first side element transversely to the channel, and at least one folding device movable transversely to the channel for the folding of the film around the fiber bundle.