Abstract: In a two-stage apparatus for burning a fuel and a combustion-sustaining gas such as air, the first stage (12) comprises pulse combustors (16) supplied with an excess of fuel. The excess fuel is burned in a second combustion stage (14) with gas that is aspirated using the backflow through the aerodynamic valve inlet (20) of the pulse combustor and delivered, e.g. via a duct (40), to the second combustion stage. Heat is extracted from the first stage using a heat-transfer medium (46) such as water. Heat is also extracted from the combustion products of the second stage to produce substantially cooled combustion products, a portion of which recirculates, e.g. through the ducts (54) and (58) and an aerodynamic valve (60), to each pulse combustor. The rest of the cooled combustion products are exhausted, e.g. at (64), with only a low content of objectionable compounds formed from nitrogen in the fuel and the combustion-sustaining gas.