A correlated dynamic adaptive chemistry and transport (CO-DACT) method is developed to accelerate numerical simulations with detailed chemistry and transport properties in a reactive flow. Different sets of phase parameters, which govern the transport properties and chemical reaction pathways, respectively, are proposed to identify the correlated groups for transport properties and reaction pathways in both temporal and spatial coordinates. The correlated transport properties and reduced chemical mechanisms in phase space are dynamically updated by different user-specified threshold values. For the calculation of detailed transport properties, the mixture-averaged diffusion model is employed. For the on-the-fly generation of reduced chemistry, the multi-generation path flux analysis (PFA) method is used. In the present method, the chemical reduction and transport properties calculation are only conducted once for all the computation cells in the same correlated group within the pre-specified thresholds. Therefore, without sacrificing accuracy within the range of uncertainty of mechanisms and transport properties, the CO-DACT method can eliminate all redundant chemistry reductions and transport properties calculations in temporal and spatial coordinates when the transport properties and chemical reaction pathways are correlated due to the similarities in phase space. The CO-DACT method is further integrated with the hybrid multi-timescale (HMTS) method to achieve efficient integration of chemistry. Simulations of outward propagating spherical premixed flames and one dimensional (1D) diffusion ignitions of a jet fuel surrogate mixture, as well as an unsteady spherical propagating diffusion flame of a DME/air mixture are conducted to validate the present algorithm. The impact of the selection of threshold values as well as the dependence of numerical errors on pressure and equivalent ratio are also examined. The results demonstrate that the CO-DACT method can increase the computation efficiency for transport properties by at least two-order of magnitudes. Moreover, it is robust, accurate, and improves the overall computation efficiency involving a large kinetic mechanism. (C) 2017 The Combustion Institute. Published by Elsevier Inc. All rights reserved.