Tool-switching device for a machine for measuring coordinates wherein the tool is fastened on the tool-carrier and held by the action of elements exerting an axial force. The locking force is taken over symmetrically by the elements of a Boys connection, which increases the repeatability of the connection; in one embodiment, two pins or spheres are driven by a sliding bushing provided with two “V”-shaped slits or with two lateral gorges. In the subsequent embodiments, the pins are replaced by spheres, by levers or by a stirrup.