  The article investigates systems of differential-difference equations of
hyperbolic type, integrable in sense of Darboux. The concept of a complete set
of independent characteristic integrals underlying Darboux integrability is
discussed. A close connection is found between integrals and characteristic
Lie-Rinehart algebras of the system. It is proved that a system of equations is
Darboux integrable if and only if its characteristic algebras in both
directions are finite-dimensional.
