A constant velocity universal joint comprises an outer joint element having grooves on its spherical inner surface. An inner joint element is positioned within the outer joint element and is provided with grooves on its spherical outer surface to form pairs of opposed grooves with the grooves on the outer joint element. A ball is positioned in every pair of opposed grooves and a cage disposed between the two joint elements retains the balls in a plane perpendicular to the axis of the cage. The cage is guided within the outer joint element by a spherical surface on the outer face of the cage and is guided with respect to the inner joint element by a spherical surface on the inner face of the cage. To facilitate assembly in the joint without weakening structural strength of the cage, the cage is provided with transverse notches or grooves in two diagonal positions. Each groove is formed at a ball aperture and has a width and a depth so as to be capable of receiving a ridge between adjacent grooves on the outer joint element.