Multi-stage combustion technology combined with nitrogen-enriched air technology for controlling the combustion temperature and products to extend the maintenance and lifetime cycles of materials in contact with combustion products and to reduce pollutants while maintaining relatively high combustion and thermal cycle efficiencies. The first stage of combustion operates fuel rich where most of the heat of combustion is released by burning it with nitrogen-enriched air. Part of the energy in the combustion gases is used to perform work or to provide heat. The cooled combustion gases are reheated by additional stages of combustion until the last stage is at or near stoichiometric conditions. Additional energy is extracted from each stage to result in relatively high thermal cycle efficiency. The air is enriched with nitrogen using air separation technologies such as diffusion, permeable membrane, absorption, and cryogenics. The combustion method is applicable to many types of combustion equipment, including: boilers, burners, turbines, internal combustion engines, and many types of fuel including hydrogen and carbon-based fuels including methane and coal.