A machine (1) configured to remove and mount a tyre from and on a respective rim of a vehicle wheel (2), comprises: an operating arm (4) directed along a longitudinal orientation; a head (5) supported by the operating arm (4); a first tool and a second tool. The first tool is connected to the head (5) and projects in a first direction; the second tool is connected to the head (5) and, in a first operating configuration of the head (5), is disposed in a first position where it projects in a second direction, opposite to the first direction. The second tool is pivoted to the head (5) to rotate about an axis of tilt (406′) transverse to the longitudinal orientation (402) to move from the first position to a second position, corresponding to a second operating configuration of the head (5) and tilted upside down relative to the first position, to project in the first direction.