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.

For the structure functions of the quark propagator, the asymptotic behavior is obtained for general, linear, covariant gauges, and in all directions of the complex k 2 -plane. Asymptotic freedom is assumed. Corresponding previous results for the gauge field propagator are important in the derivation. Except for coefficients, the leading asymptotic terms are determined by one-loop or by two-loop information, and are gauge independent. Various sum rules are derived.