  The Caswell-Wilczek analysis on the gauge dependence of the effective action
and the renormalization group functions in Yang-Mills theories is generalized
to generic, possibly power counting non renormalizable gauge theories. It is
shown that the physical coupling constants of the classical theory can be
redefined by gauge parameter dependent contributions of higher orders in
$\hbar$ in such a way that the effective action depends trivially on the gauge
parameters, while suitably defined physical beta functions do not depend on
those parameters.
