A headlight for motor vehicles is provided that includes an optical element, which is connected to a support element by at least one ball-and-socket joint. The ball-and-socket joint has a spherical ball and a spherical socket. The socket encloses the ball with socket segments and is inserted together with the ball into a receptacle, and contacts, via its socket segments, the inside of the receptacle. The socket contacts the bottom of the receptacle with a base, and has on the other side freestanding elastic socket segments that enclose the ball. Elastic detent elements of the receptacle engage behind the base of the socket and retain the socket axially in the receptacle.