Abstract: A method of at least partially burning a hydrocarbon and/or carbonaceous fuel in order to yield hot gaseous products of relatively low pollutant content, in which the fuel is partially burned in a first stage flame under such conditions that the partially combusted fuel has a temperature in the range 800.degree. to 1600.degree. C., (e.g., about 1150.degree. C.) and is substantially free of smoke and/or carbon, bringing the partially combusted fuel at 800.degree. to 1600.degree. C. into contact with a substantially non-volatile catalyst (19) which is active for reducing the amount of NO.sub.x in the partially combusted fuel, and then at least partially burning the partially combusted fuel, after contact with the catalyst (19) in a second stage flame to yield the desired low pollutant hot gaseous products. Preferably one or both of the said flames burns in contact with a substantially non-volatile catalyst (25, 23) to reduce still further the NO.sub.x content of the final gaseous products.