Abstract: In this pipe connection, the pipe end part (5) is pressed, as a result of cold-forming in zones, by means of a press ring (4) to be displaced axially, to form a positive leak-proof connection with a connection piece (1) inserted into the pipe end part and belonging to a pipe fitting (2). A sleeve (3) to be pushed onto the pipe end part is provided with an annular outer bead (7) and, when the press ring is pressed on, is deformed in such a way that the sleeve material is displaced radially inwards in the bead zone (8), the pipe end part and connection piece acquiring an annular recess (9). Moreover, the press ring (4) has at its rear end an annular inner bead (10) which at the same time displaces the sleeve material radially inwards at the rear sleeve end, as a result of which further pressing takes place at the end (12) of the connection piece (1). The gap between the pipe and connection piece is thus closed, so that no crevice corrosion can occur.