Abstract: To produce a pipe connection, one of the pipes that are to be interconnected has a pipe end that is widened in a cuplike manner, in which the pipe end of the other pipe is positively lodged. Before the two pipe ends are fixed together, a metallic clamping ring, the inside diameter of which is less than the outside diameter of the outer pipe end, is placed onto the inner pipe end. With the aid of a suitable assembly tool, the clamping ring is then pressed onto the outer pipe end. This produces a radial compression of the interengaging pipe ends, and simultaneously a radial expansion of the clamping ring in the elastic range. So that the clamping ring in the assembled position produces a deformation and clamping of the interengaging pipe ends over as great an axial length as possible, the outer surface of the clamping ring has an encircling reduction in the central section between the shorter substantially cylindrical end sections.