  The conformal symmetry in the Liouville theory is analysed by using the
Hamiltonian light--front formalism. The boundary conditions of dynamical
variables are seen to involve an arbitrary function of time, so that the
standard methods for studying gauge symmetries do not work. We develop a
general method for constructing the gauge generators, which enables a
consistent treatment of the boundary conditions present in the case of the
conformal symmetry.
