Symmetries in two-dimensional dilaton gravity with matter

The symmetries of generic two-dimensional (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.