  We discuss anomalies associated with outer automorphisms in gauge theories
based on classical groups, namely charge conjugations for $SU(N)$ and parities
for $SO(2r)$. We emphasize the inequivalence (yet related by a flavor
transformation) between two versions of charge conjugation for $SU(2k)$,
$SO(2r)$, and $E_6$ symmetries. The subgroups that commute with the outer
automorphisms are identified. Some charge conjugations can lead to a paradox,
which is resolved by the observation that they are anomalous and hence not
symmetries. We then discuss anomaly matching conditions that involve the charge
conjugations or parities. Interesting examples are given where the charge
conjugation is spontaneously broken.
