  We determine all the terms that are gauge-invariant up to a total spacetime
derivative ("semi-invariant terms") for gauged non-linear sigma models.
Assuming that the isotropy subgroup $H$ of the gauge group is compact or
semi-simple, we show that (non-trivial) such terms exist only in odd dimensions
and are equivalent to the familiar Chern-Simons terms for the subgroup $H$.
Various applications are mentioned, including one to the gauging of the
Wess-Zumino-Witten terms in even spacetime dimensions. Our approach is based on
the analysis of the descent equation associated with semi-invariant terms.
