the invention relates to a winding machine , on which , in alternation , a wound package is wound in a winding position of a spindle , while at the same time a completely wound package is removed from another spindle . with winding machines according to the prior art , the completely wound package must be removed quickly before the other wound package has reached a critical diameter to avoid a collision of their lateral faces . according to the invention , a shifting device shifts the completely wound package before or during the winding process of the wound package such that the axial extensions of the wound packages have no overlap . the collision of the wound packages can thus be prevented as the diameter of the wound package increases , whereby a more compact design with a smaller spacing of the spindles is made possible and an operator has more time to remove the completely wound spool .