A sticky label is applied to positions lying in two different planes on the surface of an object carried through the machine (1) on a conveyor. Individual labels are stored in a dispenser device (17). A manipulator device (16) for receiving, holding and applying the dispensed labels is mounted on a rotatable arm (13). This manipulator device is mounted in the free end (130) of the arm and can be moved at right angles to the arm length axis (4).