abstract: We prove that the affine unipotent and ergodic diffeomorphisms of nilmanifolds $T$ have asymptotic orthogonal powers, that is all ergodic joinings of the the products $ T r \otimes T s $ converge to the product joining, when the relatively prime integers $ r $ and $ s $ go to infinity. In collaboration with K. Fr{\c a}czek, J. Ku{\l}aga-Przymus and M. Lema{\'n}czyk