A new method to treat chemical reactions in combustion problems with detailed mechanisms is developed. The method is called in situ adaptive tabulation in principal directions (ISATPD). The tabulation is done in situ during combustion calculations and is made in the first few principal directions of the composition space. The integration of the governing equations of chemical reactions is made using detailed mechanisms. Test calculations of the premixed pairwise mixing stirred reactor (PPMSR) are performed for methane/air combustion with a skeletal mechanism consisting of 16 species and 40 reactions, and for natural gas combustion with the GRI 2.11 mechanism consisting of 49 species and 279 reactions. Results show that this method has excellent accuracy (for all species) and efficiency. A speedup in performing chemistry of 1,665 is obtained for the methane/air combustion system with the skeletal mechanism. The speedup will increase as the calculation continues since less integrations will be performed.