In a gas turbine group which consists essentially of a compressor (2), a first combustion chamber (3), a first turbine (4), a second combustion chamber (5) and a second turbine (6), the first combustion chamber (3) is configured as an annular combustion chamber. This annular combustion chamber (3) is operated by a number of premixing burners (11) which are distributed at the periphery. The first turbine (4) is designed in such a way that its exhaust gases have a temperature level which is above the self-ignition temperature of the fuel (13) used in the second combustion chamber (5). This second combustion chamber (5) consists of a burnerless, annular combustion space in which a number of vortex-generating elements (14) are integrated. The turbomachines, namely compressor (2), first turbine (4) and second turbine (6) are disposed on a rotor shaft (1), this rotor shaft (1) being supported in two bearings (9, 15).