Stripping device for insulation layer

A device for stripping conductor ends contains two stripping devices arranged in a mouth formed by clamping jaws. The two stripping devices can be displaced in a longitudinal direction of the mouth. At least one of the stripping devices includes a stack of laminates which are located side by side. The stack can be moved transversely with respect to the longitudinal direction of the mouth and has cutting edges which penetrate into insulation of a conductor which is held by the clamping jaws when the mouth is closed. A laminate guidance device is matched to the profile of the conductor and controls the laminate transverse movement in a corresponding manner. The laminate guidance device is located on the rear side of the laminate stack.