Abstract: The invention concerns a bellows device (17) including an elastic bellows (19) adapted to be connected at a first end to a first rotary member (9) and the second end of which has a portion (24) turned back axially outwards, the free end of this turned back portion being adapted to be fixed to a second rotary member (11). The device includes a rigid member (21) for stabilizing the bellows (19) including a radially external connecting part adapted to assure axial retention of said member (21) relative to the second rotary member (11) and a radially internal part (33) adapted to extend axially towards the turned back portion (24), inside the latter, and to have an annular surface facing the bellows (19) that is free of sharp edges.