A new, non perturbative, eikonal method called the "quasi abelian limit" (Q
AL) is suggested for high energy quark (nucleon) scattering involving the e
xchange of all possible, non interacting, non abelian gluons (mesons). With
this method, those functional integrals defining, e.g., the exchange of co
lor cooordinates in quark-quark scattering, are replaced by a finite number
of quadratures over a subset of their coordinates. Mathematically, this pr
ocedure is not rigourous, because an unjustified interchange of limits has
been performed. physically, it corresponds to the observation that the non
perturbative sum over all color-moment fluctuations can vanish at arbitrari
ly high energies. The QAL generates a result in agreement with a corrected,
"contiguity" calculation, when the latter is summed over all perturbative
orders.