The dilution of fuel-air mixtures by exhaust gases (mainly CO2, H2O, and CO) affects the kinetics of combustion. This dilution is used in gas turbines and flameless combustor to reduce pollutant emissions, particularly nitrogen oxides (NOx). Therefore, studying the effect of these compounds on the kinetics of oxidation of fuels such as natural gas and hydrogen is needed. The oxidation of H-2 and that of CH4 were studied experimentally in a fused silica jet-stirred reactor (JSR) from fuel-lean to fuel-rich conditions, over the temperature range 800-1300 K. The experiments were repeated in the presence of 10% in mol of H2O. A detailed chemical kinetic modeling of these experiments and of literature data (ignition delays, flame speed) was performed using a detailed kinetic reaction mechanism. Good agreement between the data and this modeling was obtained. Sensitivity and reaction paths analyses were used to respectively delineate the influencing and important reactions for the kinetics of oxidation of the fuels in the presence of H2O. The proposed kinetic reaction mechanism helps us to understand the inhibiting effect of water vapor on the oxidation of hydrogen and methane. The effect of H2O on NOx formation under gas turbine conditions was also investigated numerically, showing the reduction of NOx emissions is mainly due to dilution and thermal effects.