Apparatus for mounting a tyre (P) on a rim (C) of a wheel (R) and/or for removing a tyre (P) from a rim (C) of a wheel (R) of a vehicle, comprising: a base having a support for receiving and rotating the wheel (R); a frame joined to the base and having an upright with a longitudinal axis (L) substantially parallel to an axis of rotation (A) of the wheel (R); a support arm associated with the upright and movable in a direction substantially parallel to the axis of rotation (A) of the wheel (R); a tool for operating on the wheel (R), said tool being mounted on the support arm ; a hydraulic or pneumatic actuator able to move the support arm along the direction substantially parallel to the axis of rotation (A) of the wheel (R), the hydraulic or pneumatic actuator comprising a piston sliding inside a jacket defining therein a first chamber upstream of the piston and a second chamber downstream of the piston; characterized in that at least one pressure sensor is associated with said hydraulic or pneumatic actuator , wherein: said at least one pressure sensor is configured to determine a first pressure relating to the first chamber and a second pressure relating to the second chamber, said at least one pressure sensor is able to send a signal representing contact between the tool and the wheel (R) to a control unit , and the control unit is able to control the hydraulic or pneumatic actuator and/or a further actuator , associated with the support arm , so as to move the tool along a trajectory determined by the control unit , depending on the signal representing the contact between the tool and the wheel (R). a base having a support for receiving and rotating the wheel (R); a frame joined to the base and having an upright with a longitudinal axis (L) substantially parallel to an axis of rotation (A) of the wheel (R); a support arm associated with the upright and movable in a direction substantially parallel to the axis of rotation (A) of the wheel (R); a tool for operating on the wheel (R), said tool being mounted on the support arm ; a hydraulic or pneumatic actuator able to move the support arm along the direction substantially parallel to the axis of rotation (A) of the wheel (R), the hydraulic or pneumatic actuator comprising a piston sliding inside a jacket defining therein a first chamber upstream of the piston and a second chamber downstream of the piston; characterized in that at least one pressure sensor is associated with said hydraulic or pneumatic actuator , wherein: said at least one pressure sensor is configured to determine a first pressure relating to the first chamber and a second pressure relating to the second chamber, said at least one pressure sensor is able to send a signal representing contact between the tool and the wheel (R) to a control unit , and the control unit is able to control the hydraulic or pneumatic actuator and/or a further actuator , associated with the support arm , so as to move the tool along a trajectory determined by the control unit , depending on the signal representing the contact between the tool and the wheel (R). said at least one pressure sensor is configured to determine a first pressure relating to the first chamber and a second pressure relating to the second chamber, said at least one pressure sensor is able to send a signal representing contact between the tool and the wheel (R) to a control unit , and the control unit is able to control the hydraulic or pneumatic actuator and/or a further actuator , associated with the support arm , so as to move the tool along a trajectory determined by the control unit , depending on the signal representing the contact between the tool and the wheel (R). <EOS>