Abstract: Method and apparatus for safely combusting a fuel in such manner that very low levels of NO.sub.x and CO are produced. The apparatus comprises an inlet line (12) containing a fuel and an inlet line (18) containing an oxidant. Coupled to the fuel line (12) and to the oxidant line (18) is a mixing means (11,29,33,40) for thoroughly mixing the fuel and the oxidant without combusting them. Coupled to the mixing means (11,29,33,40) is a means for injecting the mixed fuel and oxidant, in the form of a large-scale fluid dynamic structure (8), into a combustion region (2). Coupled to the combustion region (2) is a means (1,29,33) for producing a periodic flow field within the combustion region (2) to mix the fuel and the oxidant with ambient gases in order to lower the temperature of combustion. The means for producing a periodic flow field can be a pulse combustor (1), a rotating band (29), or a rotating cylinder (33) within an acoustic chamber (32) positioned upstream or downstream of the region (2) of combustion.