A counterflow diffusion flame between gaseous hydrogen and liquid oxygen (LOx) is studied numerically at I and 2 bar pressures. Conditions at the liquid interface are modelled using the Clausius-Clapeyron relation and the species profiles are evaluated with a one-dimensional numerical code. Complex chemistry and multicomponent transport are employed. Thermodynamic and transport properties are taken from Chemkin and the corresponding Transport packages. Typical species and temperature profiles are presented. The extinction strain rate is evaluated as a function of the inlet hydrogen temperature. This varies from 1.2 X 10(5) s(-1) at a hydrogen temperature of 20K to 6.0 X 10(5) s(-1) at a temperature of 310K, indicating that hydrogen/LOx flames are extremely resistant to strain rate. The effect of the temperature gradient on the liquid side of the interface is examined and found to be negligible. When applied to one aspect of the flame-holding in cryogenic rocket motors, these results may be used to infer that extinction by strain rate is improbable in the injector near-field, even for very low hydrogen stream temperatures. (C) 2003 The Combustion Institute. All rights reserved.