  Chiral defect fermions in the background of an external, $2n$ dimensional
gauge field are considered. Assuming first a finite extra dimension, we
calculate the axial anomaly in a vector-like, gauge invariant model for
arbitrary $n$, and the consistent anomaly in a gauge {\it variant} model with a
chiral spectrum. For technical reasons, the latter calculation is limited to
the $2+1$ dimensional case. We also show that the infinite lattice chiral
model, when properly defined, is in fact a limiting case of the above
gauge-variant model. The behaviour of this model with a dynamical gauge field
is discussed.
