An intervertebral prosthesis for insertion between adjacent vertebrae includes upper and lower prosthesis plates locatable against respective vertebrae and having opposing, concavely curved recesses therein, and a core located between the plates. The core has opposed, convexly curved surfaces received in the recesses of the plates to allow the plates to slide in articulated manner over the core. The opposed surfaces of the core and the recesses of the plates have cooperating spherical curvatures. The recess of each plate surrounds a locating peg projecting centrally from the base of the recess and is bounded by an annular rim, such that the annular rims of the plates are arranged to contact one another at a predetermined limit of sliding movement of the plates over the core. The peg locates loosely in an opening located centrally in a curved surface of the core, whereby the plates can slide over the core in all directions while the peg holds the core captive.