The blocking device of a wheel rim on a tire-mounting machine is provided with a rotating support plate having a central hole, and includes a stem for engaging with the rotating support plate, and a cursor which is slidable on the stem and which includes a conical centring body and a device for activating for moving the cursor along the stem. The device for activating includes a mechanical transmission between a collar and a motor and the coupling between the cursor and the stem is such as to prevent rotation of the cursor about the stem.