A cover assembly system is proposed for vehicles with an openable roof, the cover assembly system having at least one middle section and two side flaps that may be adjusted between a closed position and a stored position. The side flaps in their closed position together with the middle section forming a flat cover. Each side flap may be connected to a swivel bearing having a pivot axis. The side sections may be swiveled along the pivot axes between the closed position. The pivot axes extend essentially parallel to and directly adjoin the middle planar extension of the flat cover.