A surrounding bead-type collar is pressed out from the pipe material or aat least one of two pipes forming a double-pipe heat exchanger. The radial height of the collars corresponds to the difference of the radii of the interior wall of the exterior pipe and of the exterior wall of the interior pipe. The collars form axial ends of an annular flow space of a completed heat exchanger. The thus constructed pipes with collars may be slid axially and thereby mounted on one another during manufacturing. Before this mounting operation, they are plated with a Nocolok fluxing agent and are subsequently soldered together in a heating step.