The invention provides an intervertebral disk prosthesis. The prosthesis comprises:a first fixing element having both an anchoring first face for anchoring in one of the vertebrae and a co-operation second face;a second fixing element having both an anchoring first face for anchoring in the other vertebrae and a co-operation second face;a first prosthesis element having both an active first face and a co-operation second face, said co-operation faces of the first fixing element and of the first prosthesis element serving to fasten the two elements together;a second prosthesis element having both an active first face and a co-operation second face, said co-operation faces of the second fixing element and of the second prosthesis element serving to fasten the two elements together; andeach of said active faces of the prosthesis elements defining at least a portion of a spherical cap that is respectively concave or convex.