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• Identification of phase instability for diffusion flames on both stable and middle branches. • Analysis of mass and heat diffusion and its impact on presence of unstable phase. • Sensitivity study on the effects of pressure, inlet temperature and diffusion model. The single-phase instability of high-pressure, steady, laminar counterflow diffusion flame is studied using the Vapor–Liquid Equilibrium (VLE) theory. The a posteriori study focuses on the identification of the potentially unstable regions emerging throughout the full combustion states represented by the high-pressure counterflow diffusion flame solution; a specific emphasis is placed on the middle branch solutions which are characteristic of intermediary combustion states. The a posteriori analysis provides useful bounds on the multicomponent phase separation. We use a mixture-fraction space flamelet formulation with real-fluid thermodynamics; the results compare favorably to both a spatial-based flamelet and a two-dimensional direct numerical simulations (DNS) solution, at high-pressure conditions. The a posteriori , single-phase instability for a high-pressure LO2/GH2 flame is investigated by investigating the effects of operating pressure and inlet temperature on the flame structure; then the analysis is extended to a LO2/GCH4 flame to evaluate the fuel effect. It is found that a single-phase instability can appear at both the fuel and oxidizer inlets, and its location and extent is determined by the water vapor concentration and, more importantly, temperature. For the flamelets in the upper burning branch, the size and location of unstable region is nearly invariant to the scalar dissipation rate, while for the flamelets in the middle branch, the instability region near the fuel inlet expands significantly with the decrease of chemical reactivity. [ABSTRACT FROM AUTHOR]