An apparatus for removing a sheath of electrical conductors of a preferably multicore cable (K), preferably a film located between a shielding or an insulation and the inner conductors, comprising a cutting apparatus with at least one clamping device for clamping the cable (K) axially and rotationally along a longitudinal axis of the cable, and a knife arrangement for scoring the sheath, further comprising a stripping device (A) for the at least partially scored sheath, which device is integrated in the apparatus and comprises stripping means designed to produce a non-positive connection with the sheath and exert a force on the sheath along the longitudinal axis parallel to the cable axis, and wherein the stripping device (A) comprises at least one application arrangement for at least one adhesive tape , at least one adhesive tape as stripping means, and means for stripping the at least one adhesive tape with the sheath sticking to it in the lengthwise direction of the cable (K), characterized in that the knife arrangement is arranged rotatably around the longitudinal axis, the application arrangement comprises at least one guide jaw which is automatically movable radially towards the cable (K) extending along the longitudinal axis and away from the cable (K), and is movable in the longitudinal direction of the cable (K), to provide guidance for the adhesive tape and to press the adhesive tape against the sheath, and that the guide jaw is a rigid body, preferably made of metal, of which a section bears on the cable (K) via the adhesive tape , which section is furnished with an elastic layer, preferably in the form of an insert, adapting it to press against the adhesive tape over the largest possible area while gently enclosing the cable (K). comprising a cutting apparatus with at least one clamping device for clamping the cable (K) axially and rotationally along a longitudinal axis of the cable, and a knife arrangement for scoring the sheath, further comprising a stripping device (A) for the at least partially scored sheath, which device is integrated in the apparatus and comprises stripping means designed to produce a non-positive connection with the sheath and exert a force on the sheath along the longitudinal axis parallel to the cable axis, and wherein the stripping device (A) comprises at least one application arrangement for at least one adhesive tape , at least one adhesive tape as stripping means, and means for stripping the at least one adhesive tape with the sheath sticking to it in the lengthwise direction of the cable (K), the knife arrangement is arranged rotatably around the longitudinal axis, the application arrangement comprises at least one guide jaw which is automatically movable radially towards the cable (K) extending along the longitudinal axis and away from the cable (K), and is movable in the longitudinal direction of the cable (K), to provide guidance for the adhesive tape and to press the adhesive tape against the sheath, and that the guide jaw is a rigid body, preferably made of metal, of which a section bears on the cable (K) via the adhesive tape , which section is furnished with an elastic layer, preferably in the form of an insert, adapting it to press against the adhesive tape over the largest possible area while gently enclosing the cable (K). <EOS>