  The Cauchy problem for two dimensional difference wave operators is
considered with potentials and initial data supported in a bounded region. The
large time asymptotic behavior of solutions is obtained. In contrast to the
continuous case (when the problem in the Euclidian space is considered, not on
the lattice) the resolvent of the corresponding stationary problem has
singularities on the continuous spectrum, and they contribute to the
asymptotics.
