Abstract: The invention relates to a connection of a metal pipe with a metal sleeve by means of cold-pressing deformation. The metal sleeve on its inside shell is provided with a pipe limit stop and the portion of the sleeve to be connected with the pipe end, along its inside shell, exhibits deformations before the pressing process. In one embodiment, the deformations of the inside shell of the metal sleeve are formed as ribs extending around the axis of the sleeve. The ribs on the inside shell of the metal sleeve are spaced at varying distance from each other. In another exemplary embodiment, the deformation of the inside shell of the sleeve has a convex curvature so that a frictionally-engaged connection is created after pressing.