  In this paper we study the Ellis semigroup of a d-step nilsystem and the
inverse limit of such systems. By using the machinery of cubes developed by
Host, Kra and Maass, we prove that such a system has a d-step topologically
nilpotent enveloping semigroup. In the case d=2, we prove that these notions
are equivalent, extending a previous result by Glasner.
