In a pivoting mounting for an optical element of a motor vehicle headlamp, of the kind comprising a seating in which a ball head at the end of a retaining and/or adjusting bar or screw for the headlamp is received, the seating is defined by two cup elements shaped as half shells and together defining a substantially spherical cavity. This cavity is open to the outside through a flared aperture in the front face of the cup elements. The two cup elements are hinged together so as to open and close the cavity, and are provided with a snap-fitting device comprising, on one of the cup elements, a projecting tab having a finger pad and a locking shoulder for cooperation with a further locking shoulder formed on the other cup element. The rear of one of the cup elements is joined to a base member having a rear face from which snap-fitting means, in the form of mutually overlying pairs of snap catches, are carried. These catches engage in snap-fitting relationship against retaining shoulders formed around a mounting hole in a headlamp element, against which the rear face of the base member abuts when fitted.