Numerical study was conducted to clarify effects of added $CO_2$ for the downstream interaction between $H_2$-air and CO-air premixed flames in counterflow configuration. The reaction mechanism adopted was Davis model which had been known to be well in agreement with reliable experimental data. The results showed that both lean and rich flammable limits were reduced. The most discernible difference between the two with and without having $CO_2$ addition into $H_2$-air and CO-air premixtures was two flammable islands for the former and one island for the latter at high strain flame conditions. Even a small amount of $H_2$, in which $H_2$-air premixed flame cannot be sustained by itself, participates in CO oxidation, thereby altering the CO-oxidation reaction path from the main reaction route $CO+O_2{ ightarrow}CO_2+O$ with a very long chemical time in CO-air flame to the (H, O, OH)-related reaction routes including $CO+OH{ ightarrow}CO_2+H$ with relatively short chemical times. This intrinsic nature alters flame stability maps appreciably. The results also showed that chemical effects of added $CO_2$ suppressed flame stabilization. Particularly this phenomenon was appreciable at flame conditions which lean and rich extinction boundary was merged. The detailed discussion of chemical effects of added $CO_2$ was addressed to the present downstream interaction.