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.