A pair of spherical gears connects the intersecting shafts of a CV-joint. One gear has internal teeth, and the other has external teeth. The gear design is based on pitch circles that are great circles on theoretical pitch spheres that are concentric and have identical radii. The gear teeth are preferably straight-sided. Individual smaller construction spheres are arranged in a circle so that the points of tangency between successive smaller spheres are all positioned on the circumference of the identical pitch circles of the gears and are all also positioned on the respective pitch circles of each successive smaller construction sphere. The straight-sided tooth faces of the teeth of the internal gear are preferably cone shaped. The preferred embodiment uses six teeth on each gear, and the gears, while rotating at high speeds under load, can intersect throughout a continuous maximum range of 60° or more.