A device for making up a plurality of synchronously produced individual optical fibers includes a drawing installation for drawing the fibers and a take-up winder for winding up the fibers on a take-up spool. The drawing installation provides an identical and constant drawing rate for each of the fibers. The take-up winder has a compensating device to compensate for differences in speed of the fibers between the drawing installation and the take-up spool. Fluctuations of the fiber diameter during production of the fibers are avoided and the fibers are passed at a substantially constant rate to the take-up winder. A fiber bundle can be made up without influencing the drawing rate, thereby also avoiding reactions on the melting process when drawing the fibers from a heated preform. A method for making up a plurality of synchronously produced individual optical fibers is also provided.