Extinction characteristics of the two interacting premixed flames are analyzed for the effects of flame stretch and preferential diffusion using large activation energy asymptotic analysis by adopting counterflow system as a model problem. Results show that the flammable limit of the thermally interacting premixed flames is extended compared to the single flame, and the extinction mechanism is classified into weak and strong interactions. As the lewis number of the deficient species increases, the region of strong interaction diminishes which can explain the different characteristics of the extinction boundaries of the lean (rich) methane/air and butane/air flames. The influence of the flame stretch to the interaction boundaries is also studied.