A fastening device includes a clip and a retaining element. The clip has a head from which lateral wings for fastening to a panel and resilient lugs for fastening the retaining element to the clip extend laterally. The retaining element temporarily fastened inside the clip is inserted in this state inside a mounting hole or opening where final fastening of the device to the panel is performed. The retaining element has an internal cavity for disassembling the clip. The resilient lugs have a fold from which they extend so as to form inner wings which are provided with an opening. Upon insertion of the retaining element, projections of the retaining element engage inside the opening.