An experimental investigation of the oxidation of hydrogen diluted by nitrogen in presence of CO2 was performed in a fused silica jet-stirred reactor (JSR) over the temperature range 800-1050 K, from fuel-lean to fuel-rich conditions and at atmospheric pressure. The mean residence time was kept constant in the experiments: 120 ms at 1 atm and 250 ms at 10 atm. The effect of variable initial concentrations of hydrogen on the combustion of methane and methane/carbon dioxide mixtures diluted by nitrogen was also experimentally studied. Concentration profiles for O2, H2, H2O, CO, CO2, CH2O, CH4, C2H6, C2H4, and C2H2 were measured by sonic probe sampling followed by chemical analyses (FTIR, gas chromatography). A detailed chemical kinetic modeling of the present experiments and of literature data (flame speed and ignition delays) was performed using a recently proposed kinetic scheme showing good agreement between the data and this modeling, and providing further validation of the kinetic model (128 species and 924 reversible reactions). Sensitivity and reaction paths analyses were used to delineate the important reactions influencing the kinetic of oxidation of the fuels in absence and in presence of additives (CO2 and H2). The kinetic reaction scheme proposed helps understanding the inhibiting effect of CO2 on the oxidation of hydrogen and methane and should be useful for gas turbine modeling.