Intervertebral disc prostheses to implant between vertebrae of a spinal column, comprising at least two plates (1, 2), called a first (1) and a second (2) plate, articulated one on top of the other by means of at least one curved surface (11, 31), called articulation, of at least one of the plates, allowing to pivot and / or lean to the plates (1, 2) in relation to each other, by turning on, respectively, a axis substantially perpendicular to the plane of the plates and an axis substantially in the plane of the plates, said curved surfaces (11, 31) having a vertically aligned vertex with a center (C) of articulation of the prosthesis, each of the plates (1, 2) comprising edges and a surface (14, 24) known as a contact surface, intended to be in contact with a vertebral plate of one of the vertebrae between which it is planned to implant, this surface comprising cont act for each of the plates a geometric center (G1, G2) at the same distance from at least two diametrically opposite points located on the periphery of the plate (1, 2), in which: - the center (C) of articulation of the prosthesis is vertically aligned with one of the geometric centers (G1, G2) of the plates (1, 2)； - the geometric centers (G1, G2) of the plates (1, 2) are not vertically aligned and thus are displaced (D) in at least one direction perpendicular to the vertical axis of the spinal column； characterized in that the contact surfaces (14, 24) of the two plates have substantially the same dimensions and the edges of the plates (1, 2) are thus also displaced in at least one direction perpendicular to the vertical axis of the spine column.Prótesis de disco intervertebral para implantar entre vértebras de una columna espinal, comprendiendo al menos dos placas (1, 2), denominadas una primera (1) y una segunda (2) placa, articuladas la una sobre la otra por medio de al menos una superficie curvada (11, 31), denominada articulación, de al menos una de las placas, permitiendo pivotar y/o inclinarse a
