  The renormalization group flow in two--dimensional field theories is modified
if they are coupled to gravity. Beta function coefficients are changed, the
$c$--theorem is no longer strictly valid, and flows from fixed points with
central charge $c>25$ to fixed points with $c<25$ are forbidden. This is
discussed in general and at two examples, the Kosterlitz--Thouless phase
transition and the Wess--Zumino--Witten model. A possible application to string
cosmology is pointed out.
