In an endoprosthesis (11h) for a joint, the two interacting joint parts (15h, 16h) are joined by a cord-type connection piece (21h), which is attached in the vicinity of the body axis (M2h, M2h') of the convex condyle (15h) and extends through a longitudinal groove (22h) in the flexion direction of the joint. The connection piece assures a play space (31h) between the contact surfaces (19h, h', 20h, h') of joint (11h). It is protected from friction on groove wall (55h, 55h') by an elevation (50h, 43h) in concave joint part (16h). An elevation (43h, 50h) at concave joint part (16h) and a depression (49h) at convex joint part (15h) interact in such a way that the lateral movement play space between depression and elevation determines the freedom of movement with respect to the lateroflexion of the joint. In preferred forms of embodiment, thanks to the spherical surfaces at least one pair of corresponding sliding surfaces (19h, 20h; 20h') on the two condyles lie flatly on one another, under load, in any position of the joint.