In a burner for operating a combustor, the former consists essentially of a rotation generator (100), a transition piece following the rotation generator, and a mixing pipe following this transition piece. Transition piece and mixing pipe form the mixing section (220) of the burner and are located upstream from a combustion chamber (30). In the lower part of the mixing pipe is located a pilot burner system (300) which creates, among other things, a stabilization of the flame front, in particular in the transient load ranges, while minimizing pollutant emissions. A sensor (400) installed in the burner detects a flashback of the flame (80), whereupon the fuel quantity of this flame is at least temporarily reduced and at the same time the fuel quantity for the pilot burner is increased in such a way that the total fuel quantity and thus the turbine output remains constant. This measure prevents a destruction of the burner.