  In gauge field theories with asymptotic freedom, the short distance
properties of Green's functions can be obtained on the basis of weak coupling
perturbation expansions. Within this framework, the large momentum behavior of
the structure functions for gluon, quark and ghost propagators is derived. The
limits are found for general, covariant, linear gauges, and in all directions
of the complex $k^2-$plane. Except for the coefficients, the functional forms
of the leading asymptotic terms for the various structure functions are
independent of the gauge parameter. They are determined exactly in terms of
one-loop expressions (two-loop expressions in cases where one-loop terms
vanish). With the exception of the Landau gauge, the asymptotic expressions for
the gauge field propagator play an important r\^{o}le for the corresponding
limits of quark and ghost propagators. For {\it all} gauges considered, it is
the sign of the one-loop anomalous dimension coefficient of the gluon field in
Landau gauge (as a fixed point of the gauge parameter) which is of considerable
relevance for the asymptotics of the various propagators. The bounds obtained
from the asymptotic expressions, together with the analytic properties of the
structure functions, generally lead to un-subtracted dispersion
representations. In special cases, for a limited number of flavors, sum rules
are obtained for the discontinuities along the real axis. The sum rule for the
gluon propagator is a generalization of the superconvergence relation derived
previously in the Landau gauge.
