A method for generating power in a system that includes a supercritical fluid cycle (102, 202, 302) having a supercritical fluid flowing therethrough, an air-breathing cycle (104, 204) having air flowing therethrough that does not mix with the flow of the supercritical fluid, the method comprising: directing air along the air-breathing cycle to flow through a plurality of heat exchangers (132, 134, 136, 138, 232, 234, 236, 238), wherein the directing step includes combusting the air to form a combustion gas and flowing the combustion gas through at least one of the plurality of heat exchangers; compressing the supercritical fluid in a supercritical fluid compressor (110, 210) along the supercritical fluid cycle; splitting the supercritical fluid discharged from the supercritical fluid compressor into first and second discharge streams (6, 8, 46, 48) of compressed supercritical fluid, such that the first discharge stream (6, 46) of compressed supercritical fluid flows through a recuperating heat exchanger (130, 230); mixing the supercritical fluid discharged from the recuperating heat exchanger with the second discharge stream (8, 48) of compressed supercritical fluid; directing a mixture of compressed supercritical fluid through the at least one of the plurality of heat exchangers and into an inlet of a supercritical fluid turbine (114, 116, 214, 216), such that heat from the combustion gas is transferred to the mixture of compressed supercritical fluid; the method is characterized in splitting the supercritical fluid discharged from the supercritical fluid turbine into a first and second discharge streams (18, 22, 62, 66) of expanded supercritical fluid such that the first discharge stream (22, 66) of expanded supercritical fluid flows through the recuperating heat exchanger so as to heat the first discharge stream of compressed supercritical fluid; mixing the expanded supercritical fluid discharged from the recuperating heat exchanger with the second discharge stream (18, 62) of expanded supercritical fluid; and directing a mixture of expanded supercritical fluid toward the inlet of the supercritical compressor, wherein heat from the mixture of expanded supercritical fluid is transferred to the air of the air-breathing cycle, thereby cooling the mixture of expanded supercritical fluid to approximately its critical point. directing air along the air-breathing cycle to flow through a plurality of heat exchangers (132, 134, 136, 138, 232, 234, 236, 238), wherein the directing step includes combusting the air to form a combustion gas and flowing the combustion gas through at least one of the plurality of heat exchangers; compressing the supercritical fluid in a supercritical fluid compressor (110, 210) along the supercritical fluid cycle; splitting the supercritical fluid discharged from the supercritical fluid compressor into first and second discharge streams (6, 8, 46, 48) of compressed supercritical fluid, such that the first discharge stream (6, 46) of compressed supercritical fluid flows through a recuperating heat exchanger (130, 230); mixing the supercritical fluid discharged from the recuperating heat exchanger with the second discharge stream (8, 48) of compressed supercritical fluid; directing a mixture of compressed supercritical fluid through the at least one of the plurality of heat exchangers and into an inlet of a supercritical fluid turbine (114, 116, 214, 216), such that heat from the combustion gas is transferred to the mixture of compressed supercritical fluid; the method is characterized in splitting the supercritical fluid discharged from the supercritical fluid turbine into a first and second discharge streams (18, 22, 62, 66) of expanded supercritical fluid such that the first discharge stream (22, 66) of expanded supercritical fluid flows through the recuperating heat exchanger so as to heat the first discharge stream of compressed supercritical fluid; mixing the expanded supercritical fluid discharged from the recuperating heat exchanger with the second discharge stream (18, 62) of expanded supercritical fluid; and directing a mixture of expanded supercritical fluid toward the inlet of the supercritical compressor, wherein heat from the mixture of expanded supercritical fluid is transferred to the air of the air-breathing cycle, thereby cooling the mixture of expanded supercritical fluid to approximately its critical point.