a tire changing machine having a support frame , rotatable supporting device for a wheel rim , locking device for securing the wheel rim to the supporting device , a fitting tool which can be secured to an adjustable tool supporting arm carried by the support frame , and driving device for the rotatatable supporting device . the machine also includes a first and a second pressure members which can be located in diametrically opposite positions with respect to a wheel rim carried by the supporting device and are designed to act on either side of a tire on the wheel rim , and drive device for actuating , upon control , each of the first and second pressure members .