A new on-grid dynamic multi-timescale (MTS) method is presented to increase significantly the computation efficiency involving multi-physical and chemical processes using detailed and reduced kinetic mechanisms. The methodology of the MTS method using the instantaneous timescales of different species is introduced. The definition of the characteristic time for species is examined and compared with that of the computational singular perturbation (CSP) and frozen reaction rate methods by using a simple reaction system. A hybrid multi-timescale (HMTS) algorithm is constructed by integrating the MTS method with an implicit Euler scheme, respectively, for species with and without the requirement of accurate time histories at sub-base timescales. The efficiency and the robustness of the MTS and HMTS methods are demonstrated by comparing with the Euler and VODE solvers for homogenous ignition and unsteady flame propagation of hydrogen, methane, and n-decane-air mixtures. The results show that both MTS and HMTS reproduce well the species and temperature histories and are able to decrease computation time by about one-order with the same kinetic mechanism. Compared to MTS. HMTS has slightly better computation efficiency but scarifies the stability at large base time steps. The results also show that with the increase of mechanism size and the decrease of time step, the computation efficiency of multi-timescale method increases compared to the VODE solver. In addition, it is shown that the integration of the multi-timescale method with the path flux analysis based mechanism reduction approach can further increase the computation efficiency. Unsteady simulations of outwardly propagating spherical n-decane-air premixed flames demonstrate that the multi-timescale method is rigorous for direct numerical simulations with both detailed and reduced chemistry and can dramatically improve the computation efficiency. (C) 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.