Abstract: A self-aligning electrical connector system for data and/or energy transmission includes first and second connector parts and a support frame. The first connector part includes positioning pins, flat elements, and a ball socket positioned between the flat elements. The second connector part is attachable to the first connector part and includes positioning chambers engageable with the positioning pins to achieve a coarse positioning of the connector parts relative to one another. The support frame has a flat central bar including spring arms. A ball is supported by the ball socket. The first connector part is supported on the support frame by spring forces of the spring arms acting on the flat elements and is supported on the ball with the ball being rollable on the central bar whereby the first connector part is floatingly arranged on the support frame and is shiftable and tiltable relative to the support frame.