Abstract: In a reheat gas turbine engine for power generation, fuel is burnt with compressed air from a compressor in a first or primary combustor, the combustion products are passed through a high pressure turbine, the exhaust of the high pressure turbine is then burnt together with further fuel in a reheat combustor to consume the excess air, and the exhaust of the second combustor is passed through a lower pressure turbine. Excess air is supplied to the first combustor, thereby enabling so-called “lean burn” combustion for production of low levels of pollutants in the exhaust of the engine. Some turbine components of the turbines, e.g., blades or vanes, are cooled by cooling air supplies tapped off from the compressor.