  We apply a global and geometrically well-defined formalism for
spinor-dilaton-gravity to two-dimensional manifolds. We discuss the general
formalism and focus attention on some particular choices of the dilatonic
potential. For constant dilatonic potential the model turns out to be
completely solvable and the general solution is found. For linear and
exponential dilatonic potentials we present the class of exact solutions with a
Killing vector.
