A method for operating a boiler using oxygen-enriched oxidants includes introducing oxygen-enriched air, or oxygen and air, in which the oxygen concentration ranges from about 21% to about 100% by volume. Fuel and oxygen-enriched air are introduced into the combustion space within the steam-generating boiler. The fuel and oxygen-enriched air is combusted to generate thermal energy. At least a portion of the flue gases are collected and at least a portion are recirculated through the boiler. In the steam-generating boiler, the oxygen-enriched oxidant is introduced at one or more locations within the radiation zone and the convection zone of the boiler. Additionally, flue gas is collected and recirculated into one or more locations within the radiation zone and/or the convection zone of the boiler. The amount of oxygen enrichment and the total gas flow through the boiler is controlled so as to maintain the heat transfer patterns within the boiler at the originally-design specification for operation by air combustion.