System for replacing a disk between two vertebrae includes an intervertebral cage having an oblong body including at least two portions and separated by a gap extending along a curved axis and opening out through an opening at a first end of the body, and at least one introducer guide rod, a curved longitudinal core having cross-sections substantially complementary to the cross-sections of the gap so as to enable the core and the two portions of the body to slide relative to one another, elements for mounting a first end of the core to co-operate with an end of the guide rod so that the curved core projects from the end, and a push rod mounted to move relative to the guide rod so as to come into contact via one end against the end of the body in order to push the body in translation relative to the core.
