  We investigate the traveling front solutions of a nonlocal Lotka Volterra
system to illustrate the outcome of the competition between two species. The
existence of the front solution is obtained through a new monotone iteration
scheme, the uniqueness of the front solution corresponding to each propagation
speed is proved by sliding domain method adapted to nonlocal systems, and the
asymptotic decay rate of the fronts with critical and noncritical wave speeds
is derived by a new method, which is different from the single equation case.
The results demonstrate that in the long run, two weakly competing species can
co-exist.
