  We study a renormalizable, general theory of dilatonic gravity (with a
kinetic-like term for the dilaton) interacting with scalar matter near two
dimensions. The one-loop effective action and the beta functions for this
general theory are written down. It is proven that the theory possesses a
non-trivial ultraviolet fixed point which yields an asymptotically free
gravitational coupling constant (at $\epsilon \rightarrow 0$) in this regime.
Moreover, at the fixed point the theory can be cast under the form of a
string-inspired model with free scalar matter. The renormalization of the
Jackiw-Teitelboim model and of lineal gravity in $2+\epsilon$ dimensions is
also discussed. We show that these two theories are distinguished at the
quantum level. Finally, fermion-dilatonic gravity near two dimensions is
considered.
