A method and extrusion line for producing peroxide-cross-linked polyethylene pipes in an extrusion line having an extruder, a cross-linking furnace and a flue. The extruded tube is subjected to a stretching process, and the cross-linking furnace has a first heating section that extends from its inlet to an actuated deflection roller and a second heating section from the deflection roller to its outlet. The stretching process in the first heating section and the stretching process in the second heating section are monitored and regulated in such a manner that the necessary stretching of the pipe takes place primarily in the first heating section, and the stretching of the pipe in the second heating section is subjected to zero adjustment. In this case, the height of the deflection roller(s) of the cross-linking furnace and the angle of the heating sections to the horizontal plane can be height-adjustable.