Functional relations and nested Bethe ansatz forsl(3) chiral Potts model at

We obtain the functional relations for the eigenvalues of the transfer matrix of the sl (3) chiral Potts model for . For the homogeneous model in both directions a solution of these functional relations can be written in terms of roots of Bethe ansatz-like equations. In addition, a direct nested Bethe ansatz has also been developed for this case.