The present invention relates to an assembling-disassembling machine provided with a base, a rotating support device (4) for a wheel rim or tyred wheel, an upright or column element (2) extending upwards from the base, and at least one mounting/dismounting tool (6) supported by the upright or column element (2) and mounted on one end of a tool carrying arm (5) in order to transversely extend from the upright element (2). The assembling-disassembling machine also comprises rotating and shifting support means located between the upright or column element (2) and the tool-carrying arm (5) at an upper level with respect to the rotating support device (4), whereby said tool-carrying arm (5) can be rotated and shifted with respect to the upright or column element (2) between a working position, in which the tool (6) is close to the rotating support device (4) and at least one rest position far from the rotating support device (4).