A tired-wheel having a wheel-rim and a tire thereon is automatically serviced. The method includes loading the tired-wheel onto a motor-driven support mounted for rotation about an axis of rotation, centering the tired-wheel with respect to the axis of rotation, and holding it by means of the motor-driven rotatable support, urging the wheel-rim against the rotatable support by means of an urging device so as to make the tired-wheel rigid in rotation with the rotatable support, disassembling the tire from the wheel-rim by means of a pair of working arms, moving away the urging device and removing the disassembled tire, loading a new tire onto the wheel-rim, repositioning the urging device and urging the wheel-rim against the rotatable support, and mounting the new tire onto the wheel-rim by means of the pair of working arms.