The present invention relates to a machine for delivering supplied hollow bushes and for fitting individual hollow bushes to a cable, and to a corresponding method. The apparatus has a picking apparatus which can pick up hollow bushes and arrange said hollow bushes so as to be axially aligned in front of the fitting tube, and a bush fitting apparatus for fitting individual hollow bushes to a cable, wherein the bush fitting apparatus has a fitting tube which can receive and hold, on the outer surface of said tube, the hollow bushes on the inner surface thereof, and in which the cable for fitting the hollow bushes can be arranged. Furthermore, the apparatus has a delivery apparatus with a slip-over device which is capable of moving relative to the picking apparatus and by means of which the hollow bushes can be delivered from the picking device to the fitting tube, and a filling mandrel, which can protrude through the fitting tube in order to deliver the hollow bush from the picking apparatus onto the bush fitting apparatus and can withdraw from the fitting tube in order to fit the hollow bush to the cable.