  The symmetries of generic 2D dilaton models of gravity with (and without)
matter are studied in some detail. It is shown that $\delta_2$, one of the
symmetries of the matterless models, can be generalized to the case where
matter fields of any kind are present. The general (classical) solution for
some of these models, in particular those coupled to chiral matter, which
generalizes the Vaidya solution of Einstein Gravity, is also given.
