The invention relates to a device for winding up fiber strands, particularly hollow-fiber membrane strands especially for the production of dialysis filters. Said device comprises a reel support (10) that is rotatable about a main axis as well as at least two reels (7) which are rotatably mounted on the reel support, the axes of rotation of the reels extending perpendicular to the main axis of the reel support. The invention also relates to a corresponding method as well as a device for wrapping a foil (25) around a fiber strand (20). Said device comprises a receptacle encompassing a first and a second lateral element (35) and a flexible groove (30) that is mounted between the first and second lateral element (35) and is used for receiving the foil and the fiber strand. A drive unit is provided for moving at least the first lateral element transversal to the groove. Said device further comprises at least one wrapper (40, 41) which can be moved transversal to the groove and is used for wrapping the foil around the fiber strand. Also disclosed is a corresponding method.