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Steady-state structure and acoustic pressure responses of GH2-LOx diffusion flames in stagnation-point flow configuration have been studied numerically with a detailed chemistry to investigate the acoustic instabilities. The Rayleigh criterion is adopted to judge the instability of the GH2-LOx flames from amplification and attenuation responses at various acoustic pressure oscillation conditions for near-equilibrium to near-extinction regimes. Steady state flame structure showed that the chain branching zone is embedded in surrounding two recombination zones. The acoustic responses of GH2-LOx flame showed that the responses in near-extinction regime always have amplification effect regardless of realistic acoustic frequency. That is, GH2-LOx flame near-extinction is much sensitive to pressure perturbation because of the strong effect of a finite-chemistry.