Modelling of the structure and the limiting flow turning angles of an oblique detonation wave, established by a two-dimensional wedge, requires the implementation of detailed chemical kinetic models involving a large number of chemical species. In this paper, a method of reducing the computational effort involved in simulating such high-speed reacting flows by implementing a systematically reduced reaction mechanism is presented. For a hydrogen - air mixture, starting with an elementary mechanism having eight species in 12 reactions, three alternate four-step reduced reaction mechanisms are developed by introducing the steady-state approximation for the reaction intermediates HO2, O and OH, respectively. Additional reduction of the computational effort is achieved by introducing simplifications to the thermochemical data evaluations. The influence of the numerical grid used in predicting the induction process behind the shock is also investigated. Comparisons of the induction zone predicted by two-dimensional oblique detonation wave calculations with that of a static reactor model (with initial conditions of the gas mixture specified by those behind the nonreactive oblique shock wave) are also presented. The reasonably good agreement between the three four-step reduced mechanism predictions and the starting mechanism predictions indicates that further reduction to a two-step mechanism is feasible for the physical flow time scales (corresponding to inflow Mach numbers of 8 - 10) considered here, and needs to be pursued in the future.