The present invention relates to an inter-vertebral stabilizer having one or more flexible ligaments. Each flexible ligament can be engaged with two respective vertebrae and/or associated with two retaining elements, such as screws, each of which is suitable for being implanted in a respective vertebra. The present invention also relates to a process, and the associated apparatus, for determining or verifying the tension of such an inter-vertebral stabilizer before it is put into place on the spinal column. This process includes implanting, in each of the vertebrae concerned, a corresponding rigid rod extending outside the patient's body. The rods in each pair of adjacent rods are immobilized in an initial position. If the pain which is to be removed by the stabilizer persists, the process includes modifying the distance between the rods, then in immobilizing the rods in their new relative positions and in repeating the pain test. This cycle of operations is repeated, if necessary, until the pain disappears. The length to be allocated to the ligament is deduced from the distance then attained between the two rods.