A device for the mechanical stripping of at least two layers of electrical or optical cables has a stop for a fed-in conductor. The conductor is fixed in position by clamping jaws, whereupon its insulation can be severed by at least one rotating stripping blade. Disposed immediately next to each blade is a centering jaw, which centers the conductor. The jaw is radially movable relative to the blade so as to permit the penetration of the blade into the layer of insulation. The blades and the centering jaws are positioned axially and the desired cutting depth of each of at least two stripping operations is adjusted by spindles, each of which is operated by a motor which is controlled by a digital controller.