The invention relates to an adapter system for fastening bags or containers to luggage racks, particularly for fastening bags or containers to the upper side of a luggage rack by means of fixing elements for engaging around and/or engaging on and/or engaging with and particularly between struts of a luggage rack. The adapter system has at least two angle elements (2, 3) that engage on or around opposite struts and have a v-shaped, open angle of less than 90° that rests against or engages around the strut. At least one angle element (3) can be pivoted about a rotational axis and can be fixed in a position in which it positively engages around or on the strut, said fixation being reversible by means of a closing mechanism (8).
