An assembly for use in a hip joint replacement procedure which comprises a stem part for location in the intramedullary cavity of a femur, having a tapered spigot at one end, and a head part having a bearing surface defined by a part of a sphere, and a tapered bore formed in it in which the spigot is a snug fit so that the tapered surfaces of the spigot and the socket are in surface to surface contact. The distance from (i) the point on the tapered surface of the spigot at or towards its free end at which the tapered surface thereof no longer contacts the tapered surface of the bore, to (ii) the centre of the sphere which is defined by the bearing surface measured from the said point on the spigot parallel to the axis of the spigot towards the intramedullary cavity, when the spigot is received in the bore in the head part, is at least about 5 mm, with the said point on the tapered surface of the spigot being located between the centre of the sphere and the bearing surface of the head part.