A device for connecting two pipes with different external diameters using a sleeve arrangement which bridges the butt joint between the ends of the pipe facing each other. The device contains at least a fixing sleeve which can take up the clips for the two pipes, and, if necessary, a sealing sleeve which is surrounded by the fixing sleeve. High economy and safety can be achieved by the fact that each sleeve of the sleeve arrangement has cylindrical contact sections which can be adjusted to the different external diameters of the two pipes and are connected by a central section which can take a conical form to suite the diameter difference wherein the contact sections of the sleeve next to the external circumference of the two pipes can be brought into direct contact with the two pipes, and the contact sections of the fixing sleeve contain encircling mounting channels assigned to the clips, and wherein the fixing sleeve takes the form of a closed encircling ring which is suitable for three-dimensional deformation.