Addition effects of H-2 and H2O on flame structure and NOx emission behavior are numerically studied with detailed chemistry in methane-air counterflow diffusion flames. The discernible differences in flame structure and the behaviors of pollutant emissions such as CO, CO2, and NOx are compared among a pure methane flame, CH4-H-2 flames, and CH4-H-2-H2O flames. The important role of chemical effects of added H2O in flame structure and pollutant emissions is also discussed. It is seen that chemical effects of added H2O increase the maximum flame temperature for small H2O mole fraction, and this is relevant to the enhanced OH radical through the reaction step O + H2O -> OH + OH. Emission indices of CO increase and then decrease after showing a maximum in the increase of methane mole fraction for CH4-H-2 flames and in the increase of H2O mole fraction for CH4-H-2-H2O flames, while those Of CO2 increase monotonously. These behaviors are caused by the competition of the production through the reaction step HCO + H2O -> H + CO + H2O with the destruction of CO by the reaction step CO + OH -> CO2 + H. It is also found that chemical effects of added H2O reduce the CO emission index and increase the CO2 emission index. The changes of thermal NO and Fenimore NO are also analyzed for pure methane, CH4-H-2 flames, and CH4-H-2-H2O flames. In all flames, the contribution of the Fenimore mechanism in NO production is much more important. It is also shown that chemical effects of added H2O suppress NO formation mainly through the Fenimore mechanism. To facilitate the details of those NO behaviors, importantly contributing reaction steps to thermal NO and Fenimore NO are addressed for pure methane, CH4-H-2 flames, and CH4-H-2-H2O flames.