The invention relates to a device (1) and a method for making up a multiplicity of synchronously produced individual optical fibers (2), in particular multicomponent glass fibers, from a multifiber drawing installation, with a drawing installation (3) and a take-up winder (4) for winding up the fibers as a fiber bundle (2) on a take-up spool (17). In order to produce and make up the fiber bundle (2) from a multiplicity of simultaneously drawn individual fibers (2) with little effort and at low cost while maintaining predetermined quality requirements, it is proposed according to the invention that the drawing installation (3) has means for producing an identical, constant drawing rate of the fibers (2) and that the take-up winder (4) has a compensating device (5) to compensate for differences in speed of the fibers (2) between the drawing installation (3) and the take-up spool (17). This achieves the effect that each individual fiber (2) is produced under the same conditions. Fluctuations of the fiber diameter during production of the fibers (2) are avoided. An identical drawing rate of all the fibers (2) is made possible. The fibers (2) are passed at a substantially constant rate to the take-up winder (4) and further processed continuously. The speed of the drawing installation (3) is kept unchanged during the drawing of the fibers (2). In an advantageous way, the fiber bundle (2) can be made up without any reaction on the drawing rate, thereby also avoiding reactions on the melting process.