A system for replacing bone joints of substantially spherical geometry, made of biocompatible materials, comprising three articular components and a triple joint with six sliding contact surfaces for the displacements, namely: - A bone-anchoring shell made of rigid biocompatible material and having, on its concave inner face, a smooth and substantially hemispherical articular surface which is polished and has no bumps, cavities or reliefs that could cause wear of an articular mobile cup or could impede its free clearance when the latter is stressed in rotary displacement by the neck of a prosthesis for diaphyseal anchoring; - the prosthesis comprising, at the part remote from its diaphyseal anchoring part, a polished ball and a neck which is smooth, without bumps or notches, and is preferably slightly flared, in order to permit the joint physiological circumduction movement with low friction and without wear; - the mobile articular cup sliding, on the one hand, in the smooth cavity, shaped as a portion of a sphere of the bone-anchoring shell and, on the other hand, on the ball and the neck of the prosthesis, an opening of said mobile cup narrowing toward the center of said mobile articular cup, the flared part of which being designed to adapt perfectly to the flared neck of the prosthesis, in all the respective positions of the mobile components, the first joint of which is situated between the outer face of the mobile articular cup made of preferably plastic biocompatible material, and between the inside of the bone-anchoring shell made of rigid biocompatible material having a face with a substantially hemispherical concavity polished and free of bumps, cavities or reliefs that could wear said mobile cup or impede its free clearance, characterized in that the opening of said face of hemispherical concavity is situated at a distance of between 1 and 6 mm beyond the equator of said bone-anchoring shell in such a way as to form a guide skirt, and shows a rounded edge with a radius of between 1 and 5 mm, in order to avoid any abrasion of the mobile cup during its introduction into said bone-anchoring shell during surgery. - A bone-anchoring shell made of rigid biocompatible material and having, on its concave inner face, a smooth and substantially hemispherical articular surface which is polished and has no bumps, cavities or reliefs that could cause wear of an articular mobile cup or could impede its free clearance when the latter is stressed in rotary displacement by the neck of a prosthesis for diaphyseal anchoring; - the prosthesis comprising, at the part remote from its diaphyseal anchoring part, a polished ball and a neck which is smooth, without bumps or notches, and is preferably slightly flared, in order to permit the joint physiological circumduction movement with low friction and without wear; - the mobile articular cup sliding, on the one hand, in the smooth cavity, shaped as a portion of a sphere of the bone-anchoring shell and, on the other hand, on the ball and the neck of the prosthesis, an opening of said mobile cup narrowing toward the center of said mobile articular cup, the flared part of which being designed to adapt perfectly to the flared neck of the prosthesis, in all the respective positions of the mobile components,