External wall insulation system for thermally insulating an outside wall of a building, the system comprising: - an insulating layer, comprising insulating panels, attached to an outer surface of said wall; - a finishing layer attached to an outer surface of said insulating layer, wherein the insulating layer is a composite layer comprising: a high efficient insulation layer, not comprising vacuum panels, facing the wall, which high efficient insulation layer has a thermal heat transfer coefficient of less than or equal to 28 mW/m.K, and comprises a polyurethane foam layer, a poly-isocyanurate foam layer or a phenol layer, and is adapted to provide efficient insulation properties to the wall, wherein the high efficient insulation layer comprises a laminate layer, e.g. an aluminium film (15, 16), on both a first surface and a second surface of said high efficient insulation layer to achieve gas tightness of the high efficient insulation layer, and a base layer comprising a layer of polystyrene foam, such as EPS foam or XPS foam, having an open cell surface structure and facing the finishing layer, which base layer is adapted to cooperate with the finishing layer so as to provide an efficient application basis for the finishing layer, wherein the base layer of an insulating panel is connected to the high efficient insulation layer of said insulating panel. - an insulating layer, comprising insulating panels, attached to an outer surface of said wall; - a finishing layer attached to an outer surface of said insulating layer, wherein the insulating layer is a composite layer comprising: a high efficient insulation layer, not comprising vacuum panels, facing the wall, which high efficient insulation layer has a thermal heat transfer coefficient of less than or equal to 28 mW/m.K, and comprises a polyurethane foam layer, a poly-isocyanurate foam layer or a phenol layer, and is adapted to provide efficient insulation properties to the wall, wherein the high efficient insulation layer comprises a laminate layer, e.g. an aluminium film (15, 16), on both a first surface and a second surface of said high efficient insulation layer to achieve gas tightness of the high efficient insulation layer, and a base layer comprising a layer of polystyrene foam, such as EPS foam or XPS foam, having an open cell surface structure and facing the finishing layer, which base layer is adapted to cooperate with the finishing layer so as to provide an efficient application basis for the finishing layer, wherein the base layer of an insulating panel is connected to the high efficient insulation layer of said insulating panel. a high efficient insulation layer, not comprising vacuum panels, facing the wall, which high efficient insulation layer has a thermal heat transfer coefficient of less than or equal to 28 mW/m.K, and comprises a polyurethane foam layer, a poly-isocyanurate foam layer or a phenol layer, and is adapted to provide efficient insulation properties to the wall, wherein the high efficient insulation layer comprises a laminate layer, e.g. an aluminium film (15, 16), on both a first surface and a second surface of said high efficient insulation layer to achieve gas tightness of the high efficient insulation layer, and a base layer comprising a layer of polystyrene foam, such as EPS foam or XPS foam, having an open cell surface structure and facing the finishing layer, which base layer is adapted to cooperate with the finishing layer so as to provide an efficient application basis for the finishing layer, wherein the base layer of an insulating panel is connected to the high efficient insulation layer of said insulating panel.