A device for holding a part comprises a retainer member provided for applying and holding the part and having a convexly spherical surface section which is received in a concavely spherical surface section of a receptacle member. To enable movement of the spherical surface sections relative to one another, the device includes an arrangement for forming a temporary friction-free air bearing between the two surface sections, which can be removed once the surfaces of the two parts have been brought into the desired alignment and engagement to fix the receptacle and retainer members in position.