The paper is focused on the study of features of methane-hydrogen mixtures combustion in an oxy-fuel power cycle combustion chamber. The goal of the study is to find optimal combinations of thermodynamic parameters, allowing to bring the fundamental combustion characteristics, such as the normal flame propagation rate, the adiabatic combustion temperature, and the ignition delay time, closer to the parameters that are characteristic of traditional gas turbine plants. The research method includes digital experiments in the Chemkin-Pro software package using detailed kinetic patterns. The key features of the fuel combustion process in oxy-fuel power cycle combustion chambers are changing the diluent medium from atmospheric nitrogen to carbon dioxide, which is the working medium in the cycle, and applying a supercritical pressure (about 300 atm). Both changes negatively affect the combustion process intensity. To achieve the normal flame propagation rate and the maximum adiabatic temperature that are acceptable for the possible flame stabilization in the combustion zone, to exclude uneven heat release and large values of chemical underburning, the amount of CO2 diluent in the combustion zone shall be within the range of 10 to 20 % of the total amount of CO2 supplied to the combustion chamber.