  Two models of dilatonic gravity are investigated: (i) dilaton-Yang-Mills
gravity and (ii) higher-derivative dilatonic gravity. Both are renormalizable
in $2+\epsilon$ dimensions and have a smooth limit for $\epsilon \rightarrow
0$. The corresponding one-loop effective actions and beta-functions are found.
Both theories are shown to possess a non-trivial ultraviolet fixed point ---for
all dilatonic couplings--- in which the gravitational constant is
asymptotically free. It is shown that in the regime of asymptotic freedom the
matter central charge can be significantly increased by two different
mechanisms ---as compared with pure dilatonic gravity, where $n < 24$.
