Abstract: A premix burner is disclosed for operating a combustion chamber with a gaseous and/or liquid fuel, having a swirl generator for inducing a swirl flow in an incoming combustion air flow and a device for injecting fuel into the swirl flow, the swirl generator having at least two cone shell segments which fit together to form a flow body and together enclose a conically formed swirl space with a cone angle ? and air inlet slits directed tangentially to the length of the cone. At least at the downstream end region of the swirl generator, a shaped element enclosing the cone shell segments with an inside wall facing the cone shell segments is provided, and that the cone shell segments end in the inside wall in a flush manner while maintaining their shape.