  We discuss some classical and quantum properties of 2d gravity models
involving metric and a scalar field. Different models are parametrized in terms
of a scalar potential. We show that a general Liouville-type model with
exponential potential and linear curvature coupling is renormalisable at the
quantum level while a particular model (corresponding to D=2 graviton-dilaton
string effective action and having a black hole solution) is finite. We use the
condition of a ``split" Weyl symmetry to suggest possible expressions for the
``effective" action which includes the quantum anomaly term.
