The invention relates to an intervertebral disc prosthesis for the total replacement of the intervertebral disc within the lumbar and cervical spine. For a two part as well as for a three part intervertebral disc prosthesis, according to the invention, in accordance to the design of the edges of the sliding partners, there are aspects for at least one of the sliding partners, in which there is an wavelike design of the edge, as the respectively different high edge regions preferably fluently merge. A significant advantage of the two part intervertebral disc prostheses, according to the invention, compared to the present state of the art of already known prostheses, is that as a result of a transfer of load across a large surface area due to the spherical sliding surfaces, the maximal possible inclination of the sliding partners towards each other in a dorsoventral and laterolateral direction and/or the extent of axial rotation can, according to the invention, be defined through the wavelike design of the edge regions.