Abstract: A process and machine to make double-walled pipe to be connected end to end, wherein each pipe includes inner and outer tubes arranged coaxially with a ring-shaped space between them except at a connecting area at the end of the pipe where the outer tube is longitudinally retracted with respect to the inner tube. An end-wall of the outer tube is deformed to close off the ring-shaped space by the gradual application of pressure to its wall by means of a series of bars spaced in a ring around a connecting area and tilted over in a radial direction by a crown that is fixed with respect to the outer tube and onto which the bars are attached in an articulated manner.