  Unlike Einstein gravity, dilaton-Maxwell gravity with matter is
renormalizable in $2+\epsilon$ dimensions and has a smooth $\epsilon\to 0$
limit.By performing a renormalization- group study of this last theory we show
that the gravitational coupling constant $G$ has a non-trivial,ultraviolet
stable fixed point (asymptotic freedom) and that the dilatonic coupling
functions (including the dilatonic potential) exhibit also a real, non-trivial
fixed point. At such point the theory represents a standard charged
string-inspired model.Stability and the gauge dependence of the fixed-point
solution is discussed.It is shown that all these properties remain valid in a
dilatonic-Yang-Mills theory with $n$ scalars and $m$ spinors, that has the UF
stable fixed point $G^* = 3\epsilon (48+12N-m-2n)^{-1}$.In addition, it is seen
that by increasing $N$ (number of gauge fields) the matter central charge
$C=n+m/2$ ($0<C<24+6N$) can be increased correspondingly (in pure dilatonic
gravity $0<C<24$).
