  A class of two-dimensional topological conformal field theories (TCFTs) is
studied within the framework of gauged WZW models in order to gain some
insights on the global geometrical nature of TCFTs. The BRST quantizations of
topological G/H gauged WZW models (the twisted versions of SUSY gauged WZW
models) are given under fixed back-ground gauge fields. The BRST-cohomology of
the system is investigated and the correlation functions among these physical
observables are considered under the instanton back-grounds. As a consequence,
two-dimensional BF gauge theoretical aspects of TCFTs are revealed. Especially
it is shown that two correlation functions under the different instanton
back-grounds can change to each other. This process of transmutation is
described by the spectral flow. The flow is formulated as a "singular" gauge
transformation which creates an appropriate back-ground charge on the physical
vacuum of the system. The field identification problem of the system is also
discussed from the above point of view.
