  Quantum theory of dilaton gravity is studied in $2+\epsilon$ dimensions.
Divergences are computed and renormalized at one-loop order. The mixing between
the Liouville field and the dilaton field eliminates $1/\epsilon$ singularity
in the Liouville-dilaton propagator. This smooth behavior of the dilaton
gravity theory in the $\epsilon \rightarrow 0$ limit solves the oversubtraction
problem which afflicted the higher orders of the Einstein gravity in
$2+\epsilon$ dimensions. As a nontrivial fixed point, we find a dilaton gravity
action which can be transformed to a CGHS type action.
