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We investigate the existence of traveling wave solutions for a system of reaction-diffusion equations that has been used as a model for the microbial growth and competition in a flow reactor as well as for the diffusive epidemic population.For a single species model,the existence of traveling waves was proved recently.In this talk,we show the uniqueness of traveling waves for a single species model with arbitrary diffusion coefficients.We then use the continuous argument,theorem on unstable manifold,and the results from single model to prove the existence of traveling wave solutions for the model with two competing species.