Downstream interactions between lean premixed flames with mutually different fuels of syngas and CH4 have been numerically investigated particularly on and near lean extinction limits. The interaction characteristics between lean premixed (50% H2 + 50% CO)-air and CH4-air flames were shown to be quite different from those between the same hydrocarbon flames. The lean extinction boundaries were of slanted shape, thereby implying strong interactions. The weaker flames had negative flame speeds on the upper extinction boundaries, whereas the weaker flame speeds on the lower extinction boundaries were both negative and positive. The results also showed that the flame interaction characteristics did not follow the general tendency with the dependency of Lewis number in downstream interactions between the same hydrocarbon flames. Importance of chemical interaction in flame characteristics is discussed in the downstream interactions between lean premixed (50% H2 + 50% CO)-air and CH4-air flames.