A comprehensive framework has been established for studying laminar counterflow diffusion flames for general fluids over the entire regime of thermodynamic states. The model incorporates a unified treatment of fundamental thermodynamic and transport theories into an existing flow solver DMCF to treat detailed chemical kinetic mechanisms and multispecies transport. The resultant scheme can thus be applied to fluids in any state. Both subcritical and supercritical conditions are considered. As a specific example, diluted and undiluted H-2/O-2 flames are investigated at pressures of 1-25 MPa and oxygen inlet temperatures of 100 and 300 K. The effects of pressure p and strain rate epsilon(s) on the heat release rate (q) over dot(s), 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 delta(f) and heat release rate correlate well with the square root of the pressure multiplied by the strain rate as delta(f) similar to 1/root p epsilon(s) and (q) over dot(s) similar to root p epsilon(s), respectively. The strain rate at the extinction limit exhibits a quasi-linear dependence on p. Significant real-fluid effects take place in the transcritical regimes, as evidenced by the steep property variations in the local flowfield. However, their net influence on the flame properties appears to be limited due to the ideal-gas behavior of fluids in the high-temperature zone. (C) 2008 The Combustion Institute. Published by Elsevier Inc. All rights reserved.