A method of cooling a gas turbine plant and the gas turbine plant for carrying out the method

A gas turbine system (10) includes a compressor (11) sucks in which sucks in intake air (14) and to the output side available compression air (15) compressed, a combustion chamber (12) in which, using the compressor discharge air (15), a fuel (F ) (with the formation of hot gas 16) is burned, and a turbine (13) in which the hot gas (16) is expanded to perform work. In a method for cooling said gas turbine plant (10) compressed air is drawn from the compressor (11), passed as a cooling air for cooling in an internal cooling duct through thermally loaded components of the combustion chamber (12) and / or of the turbine (13), then re-cooled and subsequently compressed and added to the compressor discharge air (15). The influence of the cooling effect on the efficiency of the plant is minimized by at least a portion of the compressor discharge air (15) is used for recooling the cooling air.