  We consider a theory with gauge group $G \times U(1)_A$ containing: i) an
abelian factor for which the chiral matter content of the theory is anomalous
$\sum_{f} q^f_A \neq 0 \neq \sum_{f} (q^f_A)^3$ ; ii) a nonanomalous factor
$G$. In these models, the calculation of consistent gauge anomalies usually
found in the literature as a solution to the Zumino-Stora descent equations is
reconsidered. Another solution of the descent equations that differs on the
terms involving mixed gauge anomalies is presented on this paper. The origin of
their difference is analysed, and using Fujikawa's formalism the second result
is argued to be the divergence of the usual chiral current. Invoking
topological arguments the physical equivalence of both solutions is explained,
but only the second one can be technically called the consistent anomaly of a
classically invariant theory. The first one corresponds to the addition of
noninvariant local counterterms to the action. A consistency check of their
physical equivalence is performed by implementing the four dimensional string
inspired Green-Schwarz mechanism for both expressions. This is achieved adding
slightly different anomaly cancelling terms to the original action, whose
difference is precisely the local counterterms mentioned before. The complete
anomaly free action is therefore uniquely defined, and the resulting
constraints on the spectrum of fermion charges are the same. The Lorentz
invariance of the fermion measure in four dimensions forces the Lorentz
variation of the Green-Schwarz terms to cancel by itself, producing an
additional constraint usually overlooked in the literature. This often happens
when a dual description of the theory is used without including all local
counterterms.
