  In this paper we calculate the high--energy quark--quark scattering
amplitude, first in the case of scalar QCD, using Fradkin's approach to derive
the scalar quark propagator in an external gluon field and computing it in the
eikonal approximation. (This approach was also recently used by Fabbrichesi,
Pettorino, Veneziano and Vilkovisky to study the four--dimensional
Planckian--energy scattering in gravity.) We then extend the results to the
case of ``real'' ({\it i.e.} fermion) QCD, thus deriving again, in a rather
direct way, the results previously found by Nachtmann. The abelian case (QED)
is also discussed in the Appendix.
