  Imposing the conservation equation of the vector current for a fermion of
spin $\frac{1}{2}$ at the quantum level, a gauge anomaly for the fermion
coupling with non-Abelian vector and axial--vector fields in six--dimensional
curved space is expressed in tensorial form. The anomaly consists of terms that
resemble the chiral U(1) anomaly and the commutator terms that disappear if the
axial--vector field is Abelian.
