The well-known Jewett-Krieger theorem states that any ergodic m.p.s has a strictly ergodic topological model. Lindenstrauss showed that any ergodic measurable distal measure-preserving system has a minimal distal topological model. Obtaining in addition unique ergodicty turns out to be elusive due to subtle counterexamples. Nevertheless, we introduce certain functions which we name nilcycles whose existence guarantees a strictly ergodic distal topological model. A case where nilcycles exist is in the theory of Host-Kra factors. These factors are used in order to establish the convergence of the so called non-conventional ergodic averages introduced by Furstenberg in his proof of Szemerédi's theorem. Joint work with Zhengxing Lian.