The present invention relates to an intervertebral disc prosthesis preferablycomprising at least three pieces including an upper plate (1), a lower plate(2) and a mobile core (3) at least in relation to the lower plate (2), co-operation means (23, 33) allowing to limit or eliminate the movements of thecore (3) in relation to the lower plate (2), in translation and in rotation,respectively, about an axis substantially parallel to the lower plate (2) andabout an axis substantially perpendicular to the lower plate (2), at least onepart of the surface of at least one plate being curved and complementary witha curved surface (30) of the core (3), with which it is in contact, whereinthe top (31) of the curved surface (30) of the core (3) is off centre, in atleast one direction, in relation to the centre (32) of this curved surface(30).
