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Conclusions derived from the solution of premixed laminar flames in a stagnation point flow are important in the determination of chemically controlled extinction limits and in the ability to characterize the combustion processes occurring in turbulent reacting flows. Recent experimental, computational and theoretical work has shown that extinction of these flames can be achieved by either flame stretch or by a combination of flame stretch and incomplete chemical reaction. Extinction by flame stretch is possible when the Lewis number of the deficient reactant is greater than a critical value and extinction resulting from both flame stretch and incomplete chemical reaction is possible when the Lewis number of the deficient reactant is less han this value. In this paper we study the extinction process computationally. We model the governing conservation equations with complex transport and detailed kinetics. By employing adaptive boundary value solution methods with numerical bifurcation techniques, we generate detailed extinction curves for hydrogen-air flames in a counterflow geometry.