A connection system for connecting an accessory element to a mounting structure, in particular for connecting a fabric of an awning, tent or sun sail to a mounting structure such as a wall of a building or an outer surface of a vehicle. The connection system includes a receiving member provided on the mounting structure and defining a receiving groove extending along an extension path, and an adapter having an engaging section and a receiving section. The engaging section is configured such that an engagement with the receiving groove is caused by an insertion movement of the engaging section into the receiving groove, the insertion movement having at least a translatory component in a direction substantially perpendicular to the extension path.