Starting from the Kac--Moody structure of the WZNW model for SL(2,R) and
using the general canonical formalism, we formulate a gauge theory invariant
under local SL(2,R) x SL(2,R) and diffeomorphisms. This theory represents a
gauge extension of the WZNW system, defined by a difference of two simple WZNW
actions. By performing a partial gauge fixing and integrating out some
dynamical variables, we prove that the resulting effective theory coincides
with the induced gravity in 2D. The geometric properties of the induced gravity
are obtained out of the gauge properties of the WZNW system with the help of
the Dirac bracket formalism.Comment: LaTeX, 21 page