A covering system for insulation devices (2) on (load-bearing) structures has a connecting device (24) including a carrier surface (28) with touch-and-close fastener elements (30) that can be connected to correspondingly designed touch-and-close fastener elements (22). A reactive functional surface (36) is fitted, as a further component of the connecting device (24), on the side (34) of the carrier surface (28) directed away from the touch-and-close fastener elements (30). The reactive functional surface bonds permanently, under predeterminable shaping pressure and at a predeterminable reaction temperature, to a preferably closed-cell foam material (4; 26) of the insulation device (2).