  The nonlocal regularization method, recently proposed in
ref.\,\ct{emkw91,kw92,kw93}, is extended to general gauge theories by
reformulating it along the ideas of the antibracket-antifield formalism. From
the interplay of both frameworks a fully regularized version of the
field-antifield (FA) formalism arises, being able to deal with higher order
loop corrections and to describe higher order loop contributions to the BRST
anomaly. The quantum master equation, considered in the FA framework as the
quantity parametrizing BRST anomalies, is argued to be incomplete at two and
higher order loops and conjectured to reproduce only the one-loop corrections
to the $\hbar^p$ anomaly generated by the addition of $O(\hbar^{k})$, $k<p$,
counterterms. Chiral $W_3$ gravity is used to exemplify the nonlocally
regularized FA formalism. First, the regularized one-loop quantum master
equation is used to compute the complete one-loop anomaly. Its two-loop order,
however, is shown to reproduce only the modification to the two-loop anomaly
produced by the addition of a suitable one-loop counterterm, thereby providing
an explicit verification of the previous statement for $p=2$. The well-known
universal two-loop anomaly, instead, is alternatively obtained from the BRST
variation of the nonlocally regulated effective action. Incompleteness of the
quantum master equation is thus concluded to be a consequence of a naive
derivation of the FA BRST Ward identity.
