An intervertebral disc endoprothesis comprises two symmetrical, concave end plates with an intermediate convex spacing piece. The end plates and the spacing piece have a plane guide rim. The end plates either have an edge shoulder or an annular groove for a toroid provided on the spacing piece. Alternatively, the intervertebral disc endoprothesis comprises two asymmetric end plates and a spacing piece, however, the two areas of movement are offset by 90.degree. in relation to each other and are partial surfaces of a cylinder. In the third variation, the two symmetrical end plates are convex, the spacing piece is cylindrical as well as concave at the two ends and has a durable cover.