An intervertebral disc prosthesis for the total replacement of a intervertebral disc within the lumbar and cervical spine is disclosed. The intervertebral disc prosthesis comprises articulating sliding partners and at least one sliding surface that is between two sliding partners. Two part designs are described in which only a dorsoventral- and rotational movement is possible as a result of laterolaterally aimed, transversally arched, ventrally curved cylindrical convexity(ies) and corresponding concavity(ies), without an inclination of the sliding partners in a lateral direction. In a further design, the cylindrical articulation surfaces have no curvature, enabling a motion of the sliding partners in only a ventrodorsal direction. According to the invention, the intervertebral disk prostheses are suited for implantation from lateral and ventrolateral, particularly in revision surgeries.