  This paper is concerned with the traveling wave solutions of delayed
reaction-diffusion systems. By using Schauder's fixed point theorem, the
existence of traveling wave solutions is reduced to the existence of
generalized upper and lower solutions. Using the technique of contracting
rectangles, the asymptotic behavior of traveling wave solutions for delayed
diffusive systems is obtained. To illustrate our main results, the existence,
nonexistence and asymptotic behavior of positive traveling wave solutions of
diffusive Lotka-Volterra competition systems with distributed delays are
established. The existence of nonmonotone traveling wave solutions of diffusive
Lotka-Volterra competition systems is also discussed. In particular, it is
proved that if there exists instantaneous self-limitation effect, then the
large delays appearing in the intra-specific competitive terms may not affect
the existence and asymptotic behavior of traveling wave solutions.
