The invention provides a locking device for locking together first and second elements that are movable relative to each other in an axial direction, the device comprising firstly a bushing secured to first element and including catches that are cantilevered-out in an axial direction and that are elastically deformable, and secondly an anchor portion secured to the second element and including an annular setback to receive hook-shaped ends of the catches, the device also including a locking sleeve mounted to move relative to the catches between a release position in which the catches are free to flex, and a blocking position in which the catches are prevented from flexing, wherein the locking sleeve is movable in rotation relative to the catches and includes a circumferential succession of gaps and of obstacles, such that: when the sleeve is in a first angular position corresponding to the release position, the gaps are in register with the catches which are therefore free to flex under the effect of the anchor portion moving; and when the sleeve is in a second angular position corresponding to the blocking position, the gaps are offset relative to the catches such that the catches are in register with the obstacles of the locking sleeve, thereby preventing the catches from flexing when their ends are engaged in the setback in the anchor portion.