Cervical intervertebral prosthesis with two connection plates (1, 5) for connection to in each case one of the adjacent vertebral bodies, and with a hinge core (20). The latter forms, together with one connection plate (1), a hinge with a concave hinge surface (11) on the hinge core (20) and with a complementary convex hinge surface on the connection plate (1). It bears on the other connection plate (5) via a slide surface (17) which extends substantially parallel to the direction of the connection plate (5) and which permits a relative movement in this direction and is surrounded by an edge (15) limiting this relative movement. The concave hinge surface (11) encloses the convex hinge surface within a solid angle (28) of at least 90.degree.. Its part lying within this solid angle lies inside the recess (16) surrounded by the edge (15). The stability of the prosthesis with respect to laterally incident forces is thereby increased.