Abstract: A knee support or replacement appliance having, on at least one proximal section (5) of at least one joint, a first engagement surface which extends over the length of a trajectory corresponding to a displacement from an instantaneous center of movement formed by a projection of a crossover of the ligaments in the proximal section (5) during the movement of the knee. On at least one distal section (6) of the joint, there is a second engagement surface which extends over the length of a trajectory corresponding to the displacement from the instantaneous center of movement formed by a projection of the crossover of the ligaments in the distal section (6) during the relative movement of the knee. The second engagement surface is in apposition to the first engagement surface during this movement. Retention devices (23, 24) prevent mutual slippage between the first and second engagement surfaces during the movement of the knee.