An orthopaedic joint prosthesis which is intended for the replacement of damaged or diseased joints of the human or animal body comprises a first component (2) with a rounded head portion (103) and a second component which comprises a hollow cup (1) for receiving the head portion (103) of the first component. The radius of curvature of one or both of the bearing surfaces (3, 4) changes varies that the bearing surface has a spherical portion (100) at the pole and a space (109) between the bearing surfaces (3, 4) which increases in size towards the lip of the cup (1).