An actuating device for moving a mobile cap of a thrust reverser, which includes: an actuator having a first element, such as a screw, and a second element, such as a nut, collaborating with the first element in such a way that turning the first element causes the second element to move in a translational movement. A locking piece is rotationally mobile between a locked position in which the locking piece prevents the first element from turning, and an unlocked position in which the locking piece allows the first element to turn. An unlocking piece is rotationally mobile between an active position in which the unlocking piece urges the locking piece towards the unlocked position and a passive position in which the unlocking piece allows the locking piece to return to the locked position.