The present invention relates to a flat-running device intended for being fitted on an assembly mounted on a tubeless one-piece rim for an automobile, said mounted assembly including said device, and to a method for mounting and/or removing said mounted assembly. The device according to the invention (1) includes a ring (2) with a radially internal mounting surface for the device, intended to closely match the hollow section of the rim (11), the ring having an open structure with two ends held closely facing one another by a means (5) for clamping the ring. According to the invention, at least one transverse notch (6), the two edges and the bottom of which are located under one of the ends of the ring, is formed in at least one of said side portions (3a), forming a circumferential lip which projects axially from the corresponding side wall of the ring, which includes said recess and is suitable for wedging the ring in the hollow section of the rim, such as to enable, via said notch, transverse insertion of a tool (7) such as a lever between the rim and said mounting surface in order to facilitate the operations of mounting and/or removing the device on the rim.