A torque transmission device such as a fixed constant velocity ball joint constructed as an opposed track joint and a process for producing such a device, in which the curvatures bases of the tracks of the joint deviate in their axial course from the curvatures of the ball contact lines. The process is characterized in that prior to the formation of a longitudinal profile of the joint component, the component is brought to an increased hardness by a hardening process and a diffusion layer is partially or completely removed in the region of the longitudinal profile.