Abstract: An everting catheter assembly includes a primary catheter tube inside which an everting or toposcopic element is secured spaced from the distal end of the primary catheter tube and with the open head end of the toposcopic element facing away from the open distal end of the primary catheter. The bonding of the toposcopic element to the interior of the primary catheter is effected with the use of a hollow mandrel through which the toposcopic element extends so that a short length of the toposcopic element projects out from the mandrel and is folded back over a length of the outer surface of the mandrel at the mandrel forward end. The mandrel is withdrawn into the primary catheter tube to the desired location for bonding at which point a bond is effected by means of heat conducted to the mating surfaces through the catheter wall or deposited locally by a radiative technique and heating between the mating surfaces.