  The 1--loop string background equations with axion and dilaton fields are
shown to be integrable in four dimensions in the presence of two commuting
Killing symmetries and $\delta c = 0$. Then, in analogy with reduced gravity,
there is an infinite group that acts on the space of solutions and generates
non--trivial string backgrounds from flat space. The usual $O(2,2)$ and
$S$--duality transformations are just special cases of the string Geroch group,
which is infinitesimally identified with the $O(2,2)$ current algebra. We also
find an additional $Z_{2}$ symmetry interchanging the field content of the
dimensionally reduced string equations. The method for constructing
multi--soliton solutions on a given string background is briefly discussed.
