The invention relates to an intervertebral disc prosthesis comprising at least two plates, namely first and second plates, articulated about each other by means of a curved surface, namely articulation, of at least one of the plates, each of the plates comprising a surface known as a contact surface, intended to be in contact with a vertebral plate of one of the vertebrae between which the prosthesis is intended to be inserted, this contact surface for each of the plates comprising a geometrical centre at equal distance from at least two diametrically opposite points located on the periphery of the plate, in which the geometric centres of the plates are not vertically aligned, this off-setting of the geometrical centres of the plates engendering an off-setting of the edges of the plates in at least one direction perpendicular to the vertical axis of the spinal column.