A method and an apparatus are provided for the combustion of gaseous fuel containing hydrogen or consisting of hydrogen, with a burner which provides a swirl generator, into which liquid fuel is fed centrally along a burner axis, at the same time forming a conically shaped liquid fuel column which is surrounded by a rotating combustion air stream which flows tangentially into the swirl generator and into which, additionally, a gaseous and/or liquid fuel is injected so as to form a fuel/air swirl flow which is transferred downstream of the swirl generator, along a transitional portion, into a mixing zone following the transitional portion downstream and which is ignited and burnt in a combustion chamber following downstream, at the same time forming a backflow zone.