  Covariant anomalies are studied in terms of the theory of secondary
characteristic classes of the universal bundle of Yang-Mills theory. A new set
of descent equations is derived which contains the covariant current anomaly
and the covariant Schwinger term. The counterterms relating consistent and
covariant anomalies are determined. A geometrical realization of the
BRS/anti-BRS algebra is presented which is used to understand the relationship
between covariant anomalies in different approaches.
