Abstract: The invention relates to an adjustable fixing device comprising two elements (22,34) able to be displaced the one with respect to another according to a sliding relationship during an adjustment operation for the headlight, one (22) of the said elements being fixed to the headlight and the other (34) being able to be fixed on the body (56) of the automobile by a screw (52), the device further comprising a resilient locking member (46) able to co-operate with the second element and with the screw, and comprising at least one gripping edge (46a), the tightening of the said screw initially causing the abutment of the second element against the body of the automobile then, using this abutment, the resilient deformation of the said member (46) and the bringing into engagement of the gripping edge(s) (46a) with the first element (22) for assuring the clamping of the two elements in their relative position corresponding to the desired adjustment.