The invention relates to a nucleus or inter-vertebral disc prosthesis that comprises at least two plates capable of movement relative to each other through at least one articulation interface defined by a female surface and a male surface each having an essentially spherical shape and essentially equal diameters. The two articulation surfaces are respectively intersected by surfaces that define between them a relative mobility space for the plates when the articulation surfaces are coapted; the surface intersecting the female surface being contained in the volume defined by an equatorial plane of said sphere except for said equatorial plane itself, the surface intersecting the male surface being planar or convex.