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We study the travelling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painleve integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of travelling wave solutions can be determined. In some parameter regions, exact formulas for periodic and solitary waves can be obtained while in other cases, bounded travelling wave solution are discussed.