Abstract: A cotyloidal component for a non-cemented hip prosthesis comprises a hemispherical titanium dome member and a cup of polymer material which is engaged therein to form a friction lining and to receive the spherical head of a femoral component. The titanium dome member comprises a first zone in the form of a portion of a sphere which is angularly displaced with respect to the dome member to be tangential to the equatorial edge and to bear against the roof part of the acetabulum. Disposed in projecting relationship in the zone are two stud portions for the passage therethrough of screws provided to engage into the roof part of the acetabulum and form a primary anchoring means. The zone is covered with a covering of porous titanium capable of being invaded by growing spongy bone to form a secondary anchoring. The second zone is smooth and comprises slots along meridians of the dome member to afford a capacity for elastic deformation comparable to that of the acetabulum in the region of the horns thereof.