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In this paper, we reconsider the stability of travelling wave solutions of reaction-diffusion equations with time delays, where the comparison principle does not hold. A new method will be developed to obtain the stability. Firstly, we define two auxiliary functions, and then obtain the stability of travelling wave fronts by using the known results and weight energy method. Our results complement the earlier results in this field. 

non-monotonic travelling wave fronts, weight energy method, stability.