  Consistent and covariant Lorentz and diffeomorphism anomalies are
investigated in terms of the geometry of the universal bundle for gravity. This
bundle is explicitly constructed and its geometrical structure will be studied.
By means of the local index theorem for families of Bismut and Freed the
consistent gravitational anomalies are calculated. Covariant gravitational
anomalies are shown to be related with secondary characteristic classes of the
universal bundle and a new set of descent equations which also contains the
covariant Schwinger terms is derived. The relation between consistent and
covariant anomalies is studied. Finally a geometrical realization of the
gravitational BRS, anti-BRS transformations is presented which enables the
formulation of a kind of covariance condition for covariant gravitational
anomalies.
