A locking device for locking together first and second elements that are movable relative to each other in an axial direction. The device has a bushing secured to a first element and catches that are cantilevered-out in an axial direction and are elastically deformable. The device also has an anchor portion secured to a second element and an annular setback to receive hook-shaped ends of the catches. The device also has 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.