a constant velocity universal joint for transmitting torque , having an outer joint part with outer ball tracks , an inner joint part with inner ball tracks , torque transmitting balls guided by pairs of outer and inner ball tracks positioned in corresponding meridian planes , and a ball cage which receives the balls in circumferentially distributed windows and holds same in a common plane and guides same on to the angle - bisecting plane when the joint is ariculated , with the center lines of the outer and inner ball tracks being composed of at least two differently curved portions adjoining one another , with the center lines of the ball tracks of the outer joint part each comprising convexly curved inner portions and , towards the open end , concavely curved end portions .