Relevant fuel-gas properties (XG) are measured on an ongoing basis while a gas turbine group is operating. The C2+alkane content of the fuel gas is of particular interest in this context, since it has a significant influence on the ignitability of the fuel gas in the combustion chamber. The operating parameters of the gas turbine group are acted on directly as a function of the measured fuel-gas properties. In particular, in the case of the example of a gas turbine group with sequential combustion, the distribution of the fuel mass flows ({dot over (m)}EV, {dot over (m)}SEV) between the combustion chambers (4, 8) of the gas turbine group is varied. Furthermore, if there is provision for inert media, such as water or steam, to be introduced, it is possible for the mass flow of inert media ({dot over (m)}ST) to be controlled as a function of the measured fuel properties.