The invention relates to a device for the movable connection of pipe ends, particularly of motor vehicle exhaust systems, with a flexible pipe element, such as a metal bellows, hose or the like, and with damped, spring elastic elements acting between the connection ends of the flexible pipe element. Such a device must have a simple construction, but must on the one hand compensate the relative movements acting between said connection ends and on the other ensure the necessary restoring forces for restoring the pipe element to its central position. In such a device, the invention provides for the elements to be held in expanding fastenings of supports parts, so that the linear spring characteristic of the elements is progressively modified by the expanding fastenings.