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In this work we consider the existence of traveling plane wave solutions of systems of delayed lattice differential equations in competitive Lotka-Volterra type. Employing iterative method coupled with the explicit construction of upper and lower solutions in the theory of weak quasi-monotone dynamical systems, we obtain a speed, c * , and show the existence of traveling plane wave solutions connecting two different equilibria when the wave speeds are large than c * .doi:10.3934/dcdsb.2010.14.111 fatcat:y4mkqddmvreihdaewz3bl7yqr4