An apparatus for servicing a tired wheel for motor vehicles, which comprises a tire assembling-disassembling machine provided with a rotatable motor-driven support (3) for supporting a wheel to be handled, sensor means (4, 5) for controlling both the position of, and the load on, the rotatable support (3), urging locking means (6) designed to act on the middle portion of the wheel-rim to make the wheel rigid in rotation with the rotatable support (3), detecting means (7, 7a, 7b) designed to measure the size of the wheel-rim, and program control means (EC).