A fastening device has a supporting part (9), adhesive fastening elements (25) attached to the supporting part and protruding from the supporting part (9), a shaft part (27) protruding beyond the supporting part (9), and at least one elastically resilient hooking part (19). Each hooking part (19) extends outward away from the shaft part (27) or a holding part (29) for the hooking part (19) in an initial position, forming an intermediate space (30), which is reduced as soon as the hooking part (19) is moved toward the shaft part (27) or the holding part (29) under the influence of an external application of force.