  The regularization scheme is proposed for the constrained Hamiltonian
formulation of the gauge fields coupled to the chiral or axial fermions. The
Schwinger terms in the regularized operator first-class constraint algebra are
shown to be consistent with the covariant divergence anomaly of the
corresponding current. Regularized quantum master equations are studied, and
the Schwinger terms are found out to break down both nilpotency of the
BRST-charge and its conservation law. Wess-Zumino consistency conditions are
studied for the BRST anomaly and they are shown to contradict to the covariant
Schwinger terms in the BRST algebra.
