  A possible formulation of chiral gauge theories with an anomalous fermion
content is re-examined in light of the lattice framework based on the
Ginsparg-Wilson relation. It is shown that the fermion sector of a wide class
of anomalous non-abelian theories cannot consistently be formulated within this
lattice framework. In particular, in 4 dimension, {\it all} anomalous
non-abelian theories are included in this class. Anomalous abelian chiral gauge
theories cannot be formulated with compact $\U(1)$ link variables, while a
non-compact formulation is possible at least for the vacuum sector in the space
of lattice gauge fields. Our conclusion is not applied to effective low-energy
theories with an anomalous fermion content which are obtained from an
underlying anomaly-free theory by sending the mass of some of fermions to
infinity. For theories with an anomalous fermion content in which the anomaly
is cancelled by the Green-Schwarz mechanism, a possibility of a consistent
lattice formulation is not clear.
