Abstract: The device has a screwthreaded collar 9 constituting a brake and trapped in a cavity 5 of a nut 2 with respect to which it is connected to rotate and axially movable in the cavity between an internally first position in which its screwthread 12 is in phase with the screwthread 3 of the nut and a second position in which the screwthreads are no longer in phase. The collar has splines 13 in its screwthread adapted to cooperate with splines in the screwthread 34 of a shaft 18 on which the nut is screwed so as to be immobilized in rotation on this shaft when the screwthreads of the collar 9 and the nut 2 are no longer in phase. For mounting the nut device, a tool is provided which comprises a hollow sleeve 20 defining a cavity adapted to receive the nut 2, an arrangement 29 for retaining the nut in a resilient manner and an arrangement 32 for maintaining the collar 9 in the first position at the inner end of the cavity 5 in opposition to the action of the second ring 15 when the nut is retained in the sleeve.