  We discuss the so called gauge invariant quantization of anomalous gauge
field theory, originally due to Faddeev and Shatashvili. It is pointed out that
the further non invariance of relevant path integral measures poses a problem
when one tries to translate it to BRST formalism. The method by which we
propose to get around of this problem introduces certain arbitrariness in the
model. We speculate on the possibility of using such an arbitrariness to build
series of non equivalent models of two dimensional induced gravity.
