The present invention concerns as intervertebral disc prosthesis designed to be substituted for fibrocartilaginous discs ensuring connection between the vertebra of the vertebra column or the end of the latter. The invention increases stability of such a prosthesis by providing a translation or rotation stop to its nucleus (2), or inducing an angular correction between its plates (1, 3) in contact with vertebra, or a combination of these characteristics. Such a stop is obtained by parts (6, 20) external to the nucleus, and using contact surfaces perpendicular to their contact directions. Such a stop allow a better stability together with the enforcement of such an angular correction, induced by an angle (A3) between loadbearing surfaces (21, 23) of the nucleus.