  A study of the gauged Wess-Zumino-Witten models is given focusing on the
effect of topologically non-trivial configurations of gauge fields. A
correlation function is expressed as an integral over a moduli space of
holomorphic bundles with quasi-parabolic structure. Two actions of the
fundamental group of the gauge group is defined: One on the space of gauge
invariant local fields and the other on the moduli spaces. Applying these in
the integral expression, we obtain a certain identity which relates correlation
functions for configurations of different topologies. It gives an important
information on the topological sum for the partition and correlation functions.
