The method of computational singular perturbation for the analysis and reduction of complicated chemical mechanisms has been extended to the complex eigensystem. The characteristic time scale for each species was defined by using the time scales of the independent modes weighted by radical pointers, and the time scale of each species normalized by a characteristic time scale of the system was used as a criterion in determining the quasi-steady-state species. Furthermore, for oscillatory modes the radical pointer and the importance index of the previous computational singular perturbation theory were redefined. Results show that the time scales of chemical species change dramatically and non-monotonically, and the oscillatory modes appear frequently in large chemical reaction mechanisms. The present method was then employed to generate a 4-step and a 10-step reduced mechanism for the high-temperature H-2/air and CH4/air oxidation, respectively. The validity of these reduced mechanisms were evaluated based on the responses of the perfectly stirred reactors and the one-dimensional planar propagating premixed flames. Comparisons between the reduced and detailed chemistries over a wide range of pressures and equivalence ratios show good agreement on the flame speed, flame temperature, and flame structure. A software package based on the present algorithm was compiled to generate reduced mechanisms for complex chemical mechanisms. The validity and efficiency of the present algorithm is demonstrated.