A new correlated dynamic adaptive chemistry (CO-DAC) method is developed and integrated with the hybrid multi-timescale (HMTS) method for computationally efficient and adaptive numerical simulation. The correlation of mechanisms in both time and space coordinate is proposed by using a few dominant phase parameters in low, intermediate, and high temperature chemistry. The chemical mechanisms are reduced and correlated on the fly by using the multi generation path flux analysis (PFA) method with given thresholds of correlated phase parameters. The advantages of the CO-DAC methods are that it not only provides the flexibility and accuracy for kinetic model and chemistry integration but also avoids redundant model reduction in time and space when the chemistry is correlated in phase space. In order to further increase the computation efficiency, the hybrid multi-timescale method is integrated into the CO-DAC method to solve the ordinary differential equation system of the reduced mechanisms. The simulation of ignition and unsteady flame propagation of an n-heptane and air mixture is carried out to validate and compare the proposed algorithm with the conventional ordinary differential equation solver. The results show that the present CO-DAC/HMTS algorithm is not only computationally efficient but also robust and accurate.