An apparatus for removing at least one layer of the cladding of electrical conductors or light guides is provided with at least two clamping jaws which can be moved towards the conductor for fixing the conductor in the longitudinal direction. Furthermore, a rotary stripping head is provided which comprises at least one stripping blade which can rotate about the axis of rotation of the stripping head and which can be moved radially in relation to the axis of rotation for cutting through at least one layer of the cladding of the conductor and at least two centring jaws which can be moved radially in relation to the axis of rotation of the stripping head and which are arranged directly at the blade or blades for centring the conductor in the axis of rotation of the stripping head. At least one first drive system is provided for the centring jaws and at least one separate second drive system which can be actuated independently of the first drive system is provided for the stripping blade or blades.