The invention relates to a head lamp for motor vehicles which head lamp comprises a reflector and a ball and socket assembly which enables adjusting of a reflector position and includes an adjusting member having a ball portion at an end thereof and a socket for receiving the ball portion and connected with the reflector. A head lamp of this type is disclosed in DS-OS No. 34 22 446. The reflector of this head lamp includes a socket provided with a sleeve body that interlocks with a stud projecting from the reflector. In this arrangement, a lug formed in the sleeve body interior engages a recess formed on the stud and extending transverse to the axis of the reflector. Such connection between the socket and the reflector is possible only when the reflector is made of a thermoplastic material. When the reflector is made of a thermosetting plastic material by an injection-molding process, it is not possible to form a recess extending transverse to the reflector axis. Moreover, the sleeve is connected to the socket with a radially extending arm and, therefore, when made from a thermoplastic material can be easily twisted.