The prosthesis according to the invention comprises a first component, humeral or femoral, presenting a concave surface of articulation and a second, intermediate component presenting first and second convex surfaces of articulation intended to cooperate respectively with the concave surface of articulation of the first component and with a glenoidal or acetabular concave surface of articulation. The second component is hollow and defines a volume for receiving a part of a member belonging to the first component, this part being connected to a metaphyseal part of the first component by a stem traversing an opening made in a ring of the second component mounted on a cup of which the outer surface forms the second convex surface of articulation of the second component, The first convex surface of articulation of the second component is formed on the outer surface of the ring, around the aforementioned opening.