Abstract: This rolling-contact bearing is of the type comprising an internal screw, an external nut and, therebetween, in proper engagement with said screw and nut, a plurality of threaded planet rollers held at the proper relative angular spacing by means of their trunnions engaging bores provided to this end in end rings, said rollers comprise a cylindrical central plain portion having a diameter at the most equal to the root diameter of the threads of said rollers, said plain cylindrical portion is connected through rounded fillets to the adjacent threads of the rollers. This assembly, in the case of a simple nut, affords a higher degree of rigidity with a lesser degree of losses of movement.