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 with a rounded head portion and a second component which comprises a hollow cup for receiving the head portion of the first component. The radius of curvature of one or both of the bearing surfaces changes varies that the bearing surface has a spherical portion at the pole and a space between the bearing surfaces which increases in size towards the lip of the cup.