A gas turbine plant with a compressor, a combustion chamber, a turbine and at least one heat sink is operated with a working medium in the form of a carbon dioxide / water mixture. A hydrocarbon reacts as fuel with oxygen in the combustion chamber, and the excess carbon dioxide and water thereby occurring is tapped from the circuit. The compressor and the turbine have in each case a rotor with moving blades and a casing with flow ducts and with guide blade cascades. In the compressor and / or the turbine, matching to the expansion behavior of the working medium, which is different from that of air, is brought about by modifications of the flow ducts, of the moving blades and / or of the guide blade cascades.