  It is shown that the fourth order real self-adjoint difference operator on
the Tivalent Tree admits nontrivial deformations preserving one energy level
and therefore defines a nontrinial hierarhy of the completely integrable
nonlinear systems representible through the ''L-A-B-triple''. The Laplace
transformations for these operators are also constructed. Nothing like that
exists for the second order difference operators on this tree.
