In a fuel supply system with premixing combustion, a gaseous and/or liquid fuel is introduced as a secondary flow into a gaseous, ducted main flow. The secondary flow has a substantially smaller mass flow than the main flow. The main flow is guided via vortex generators (9) of which a plurality are arranged adjacent to one another over the periphery of the duct (20), through which flow takes place, on at least one duct wall. The secondary flow is fed into the duct (20) in the immediate region of the vortex generators (9). A vortex generator (9) has three surfaces around which flow takes place freely, which surfaces extend in the flow direction, one of them forming the top surface (10) and the two others forming the side surfaces (11, 13). The fuel is fed into the duct from nozzles which are located before, behind or in the vortex generator.