Abstract: In the numerical simulations of oblique detonation wave with the detailed chemical reaction mechanism, the computation of chemical reactions costs a large amount of CPU time due to the stiffness and non-linearity. To decrease the computational costs for the chemistry computation, a series of parallel chemistry acceleration algorithms based on the reduced in situ adaptive tabulation (ISAT) method were proposed for simulations of transient compressible reacting flows. These algorithms were applied in two-dimensional 2H₂+O₂ gaseous oblique detonation computations to identify the computational performances of chemistry acceleration. Compared with the computational results by direct integration (DI), all the parallel chemistry acceleration algorithms can improve the computational efficiency of chemical reactions without the loss of computational accuracy. The maximum speedup ratio of 3.71 is obtained for the purely transposed processing (TP) algorithm. The analyses also indicate that the selection on the parallel strategies could influence the computational efficiency, which essentially is dominated by the scatter distribution rules of chemical thermodynamic states in the accessed region and the repeatable region.