A two-step chemical model for use in the numerical simulation of detonation phenomena in undiluted H2–O2 mixtures is developed in this paper. The use of an induction–time parameter is examined, and its underlying assumptions are discussed. Various previously developed approximations for the induction time are compared with the results of numerical calculations using a detailed reaction mechanism, and on this basis, a new, more–accurate approximation is proposed. The heat–releasing reactions at the end of the induction period are replaced by a suitably calibrated chemical–transformation process. The results obtained using this approach in onedimensional unsteady detonation calculations agree well with theoretical predictions for Chapman–Jouguet detonations once the steady state has been attained. When the new model was applied to the diffraction of a detonation at the exit of a detonation tube, excellent agreement between simulation and experiment was obtained.