A comprehensive framework has been established to study laminar counterflow diffusion flames for general fluids over the entire regime of thermodynamic states. The model incorporates a unified treatment of fundamental thermodynamics and transport theories into an existing model, the DMCF code, for treating detailed chemical kinetic mechanisms and multi-species transport. The resultant scheme can thus be applied to fluids at any state. Both subcritical and supercritical conditions are considered. As a specific example, diluted and undiluted H2/O2 flames are investigated at pressures of 1-250 atm and oxygen inlet temperatures of 100 and 300 K. The effects of pressure p and strain rate a on the energy release rate q̇s, extinction limit, and flame structure are examined. In addition, the impact of cross-diffusion terms, such as the Soret and Dufour effects, on the flame behavior is assessed. Results indicate that the flame thickness δ and heat release rate correlate well with the square root of the pressure multiplied by the strain rate as δf ∼/√pa and q̇s ∼ √pa. The extinction strain rate exhibits a quasi-linear dependence with p. Significant real-fluid effects take place in the transcritical regimes, as evidenced by the rapid property variations in the local flowfield. Their net influence on the flame properties, however, appears to be limited due to the ideal-gas behavior of fluids in the high-temperature zone.