Abstract: The cable is introduced into a sealing tube containing elastic sealing elements before entering the vulcanization chamber which is separated from the extruder. The elements have closed chambers which can be individually pressurized by, in each case, one line, while pressure regulation takes place by means of pressure reducing valves. Gaps can be provided between the individual chambers and they are filled by the heat transfer medium which brings about the crosslinking of the layer extruded onto cable and which passes out of the intake opening of vulcanization chamber. A leakage flow forms along the entire sealing tube and this passes through the openings of sealing elements and completely fills the annular clearance between the boundary of the opening and the cable, so that any contact between the cable and the sealing elements is at least substantially prevented. The gaps can be filled with a sealing liquid, which then forms the leakage flow instead of or together with the heat transfer medium.