An adapter system for attaching panniers or containers to luggage carriers, in particular for attaching panniers or containers to the top of a luggage carrier, has releasable fixing elements for engaging between respective structs and respective struts of the luggage carrier. The positions of the fixing elements is adjustable and are arrangeable on respective struts and/or cross members or plates or frames of the adapter system, wherein at least one strut and/or cross member and/or plate is designed with a plurality of retaining elements protruding from its surface facing the luggage carrier.