Abstract: In this process for forming an internal screw thread in a tube or link made from a composite carbon fiber based material coated with polymerized resin, the part of the tube or link comprising the screw thread is inserted in the body of the tube or the link and molded on a threaded mandrel. This part of the tube or link where the screw thread is to be formed is polymerized substantially completely and under pressure on the threaded mandrel so as to obtain a preform comprising a hard internally threaded portion extended by non polymerized fibers; an expandable mandrel is introduced into this preform; the preform is inserted inside a tube which is already polymerized or to be cured; and finally polymerization under pressure of the fibers is provided by heating and causing the mandrel to expand so as to bond them to the fibers of the tube.