The effects of preferential diffusion of hydrogen in interacting counterflow H₂-air and CO-air premixed flames were investigated numerically. The global strain rate was varied in the range 30-5917 s<SUP>-1</SUP>, where the upper bound of this range corresponds to the flame-stretch limit. Preferential diffusion of hydrogen was studied by comparing flame structures for a mixed average diffusivity with those where the diffusivities of H, H₂ and N₂ were assumed to be equal. Flame stability diagrams are presented, which show the mapping of the limits of the concentrations of H₂ and CO as a function of the strain rate. The main oxidation route for CO is CO + O₂ → CO₂ + O, which is characterized by relatively slow chemical kinetics; however, a much faster route, namely CO + OH → CO₂ + H, can be significant, provided that hydrogen from the H₂-air flame is penetrated and then participates in the CO-oxidation. This modifies the flame characteristics in the downstream interaction between the H2-air and CO-air flames, and can cause the interaction characteristics at the rich and lean extinction boundaries not to depend on the Lewis number of the deficient reactant, but rather to depend on chemical interaction between the two flames. Such anomalous behaviors include a partial opening of the upper lean extinction boundary in the interaction between a lean H2-air flame and a lean CO-air flame, as well as the formation of two islands of flame sustainability in a partially premixed configuration with a rich H₂-air flame and a lean CO-air flame. At large strain rates, there are two islands where the flame can survive, depending on the nature of the interaction between the two flames. Furthermore, the preferential diffusion of hydrogen extends both the lean and the rich extinction boundaries.