  In two space-time dimensions, we write down the exact and closed
Schwinger-Dyson equation for the gauged Thirring model which has been proposed
recently by the author. The gauged Thirring model is a natural gauge-invariant
extension of the Thirring model and reduces to the Schwinger model (in the
Abelian case) in the strong four-fermion coupling limit. The exact SD equation
is derived by making use of the transverse Ward-Takahashi identity as well as
the usual (longitudinal) Ward-Takahashi identity. Moreover the exact solution
of the SD equation for the fermion propagator is obtained together with the
vertex function in the Abelian gauged case. Finally we discuss the dynamical
fermion mass generation based on the solution of the SD equation.
