  We study the nonlocal regularization for the non-abelian gauge theories for
an arbitrary value of the gauge parameter (\xi). We show that the procedure for
the nonlocalization of field theories established earlier by the original
authors, when applied in that form to the Faddeev-Popov effective action in a
linear gauge cannot lead to a (\xi)-independent result for the observables. We
then show that an alternate procedure which is simpler can be used and that it
leads to the S-matrix elements (where they exist) independent of (\xi).
