  A model operator $H$ associated to a system of three-particles on the three
dimensional lattice $\Z^3$ and interacting via pair non-local potentials is
studied. The following results are proven: (i) the operator $H$ has infinitely
many eigenvalues lying below the bottom of the essential spectrum and
accumulating at this point, in the case, where both Friedrichs model operators
$h_{\mu_\alpha}(0),\alpha=1,2,$ have threshold resonances. (ii) the operator
$H$ has a finite number of eigenvalues lying outside of the essential spectrum,
in the case, where at least one of $h_{\mu_\alpha}(0), \alpha=1,2,$ has a
threshold eigenvalue.
