  Bethe ansatz formulation is presented for several explicit examples of quasi
exactly solvable difference equations of one degree of freedom which are
introduced recently by one of the present authors. These equations are
deformation of the well-known exactly solvable difference equations of the
Meixner-Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and
Askey-Wilson polynomials. Up to an overall factor of the so-called pseudo
ground state wavefunction, the eigenfunctions within the exactly solvable
subspace are given by polynomials whose roots are solutions of the associated
Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of
these roots.
