A process for the extrusion of peroxide crosslinked polymer parts, mainly tubes, in which the crosslinkable polymer is heated in an extruder in a controlled manner to a value above the crystallite melting point of the polymer, but below the crosslinking temperature, and fed continuously to an extrusion die to create the part and in which at least a partial crosslinking of the polymer is achieved in the extrusion die by heating of the polymer above a crosslinking temperature provision.