  We study the causality violation in the non-local phi ^{4}-theory (as
formulated by Kleppe and Woodard) containing a finite mass scale Lambda .
Starting from the Bogoliubov-Shirkov criterion for causality, we construct and
study combinations of S-matrix elements that signal the violation of causality
in the one loop approximation. We find that the causality violation in the
exclusive process \phi +\phi --> \phi +\phi grows with energy, but the growth
with energy, (for low to moderate energies) is suppressed to all orders
compared to what one would expect purely from dimensional considerations. We
however find that the causality violation in other processes such as \phi
+\phi--> \phi +\phi +\phi +\phi grows with energy as expected from dimensional
considerations at low to moderate energies. For high enough energies comparable
to the mass scale Lambda, however, we find a rapid (exponential-like) growth in
the degree of causality violation. We suggest a scenario, based on an earlier
work, that will enable one to evade a large theoretical causality violation at
high energies, should it be unobserved experimentally.
