  In this paper, we show local smooth rigidity for higher rank ergodic
nilpotent action by toral automorphisms and prove the existence of such action
on any torus TN for any even N ? 6. We also give examples of smooth rigidity of
actions having rank-one factors. The method is a generalization of the KAM
(Kolmogorov-Arnold-Moser) iterative scheme.

Dynamical Systems