  We present three types of non-conformal symmetries for a wide class of 2D
dilaton-gravity models. For the particular CGHS, or string-inspired model, a
linear combination of these symmetries is conformal and turns out to be the
well-known symmetry which allows to construct the exactly solvable
semiclassical RST and BPP models. We show that one of these non-conformal
symmetries can be converted into a conformal one by means of a suitable field
redefinition involving the metric and the derivatives of the dilaton. As a
consequence of this, and by defining a Polyakov-type term in terms of an
invariant metric under the symmetry, we are able to provide, for a generic 2D
dilaton gravity model, associated semiclassical models which are symmetry
invariant.
