  A class of integrable models of 1+1 dimensional dilaton gravity coupled to
scalar and electromagnetic fields is obtained and explicitly solved. More
general models are reduced to 0+1 dimensional Hamiltonian systems, for which
two integrable classes (called s-integrable) are found and explicitly solved.
As a special case, static spherical solutions of the Einstein gravity coupled
to electromagnetic and scalar fields in any real space-time dimension are
derived. A generalization of the `no-hair' theorem is pointed out and the
Hamiltonian formulation that enables quantizing the s-integrable systems is
outlined.
