An intervertebral prosthesis system, in particular for the cervical spine, includes at least two types of prostheses. The type of prosthesis includes a first cover plate that is configured to be connected to a first vertebral body, a second cover plate that is configured to be connected to a second vertebral body, and a prosthesis core which is held by a seat on the first cover plate and forms an articulation with the second cover plate. The core of the first type of prosthesis is movable in the anterior-posterior direction relative to the first cover plate. Mobility can also be provided in the lateral direction and rotational direction. The second type of prosthesis of the system may be the same as the first type of prosthesis or may be different, but in all examples of the second type of prosthesis the core is not movable relative to either cover plate.