  For gauge field propagators, the asymptotic behavior is obtained in all
directions of the complex $k^2$-plane, and for general, linear, covariant
gauges. Asymptotically free theories are considered. Except for coefficients,
the functional form of the leading asymptotic terms is gauge-independent.
Exponents are determined exactly by one-loop expressions. Sum rules are
derived, which generalize the superconvergence relations obtained in the Landau
gauge. (To appear in Physics Letters B)
