An intervertebral disc prosthesis designed to be substituted for fibrocartilaginous discs ensures a connection between the vertebra of the vertebra column or the end of the latter. The prosthesis includes a pair of plates spaced from each other by a nucleus. The prosthesis has increased stability by providing the nucleus with a translation or rotation stop, or by inducing an angular correction between its plates contacting vertebra, or a combination of these characteristics. The stop includes parts external to the nucleus and contact surfaces perpendicular to their contact directions. Surgical methods and instrumentation for implanting the prosthesis are also described.