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 internal teeth are either conically or spherically shaped, while the external tooth faces are cylindrical with tangential flat extensions. The spherical gears are shown on half-shafts. The preferred embodiments have six teeth on each gear, and one preferred embodiment also uses balls for the internal teeth. The gears, while rotating at high speeds under load, can intersect throughout a continuous maximum range of 60.degree. or more in any direction.