A general method of constructing canonical gauge-invariant actions is
used to establish the equivalence between 2-D induced gravity and a WZ
NW system, defined by a difference of two simple WZNW actions for the
SL(2,R) group. The diffeomorphism invariance of the induced gravity is
generated by the SL(2,R) Kac-Moody structure of the WZNW system.