  This paper is concerned with the traveling wave solutions of an
integro-difference competition system, of which the purpose is to model the
coinvasion-coexistence process of two competitors with age structure. The
existence of nontrivial traveling wave solutions is obtained by constructing
generalized upper and lower solutions. The asymptotic and nonexistence of
traveling wave solutions are proved by combining the theory of asymptotic
spreading with the idea of contracting rectangle.
