In a recent series of papers, Drager and Martin have shown global observability for a variety of particular classes of systems (including both discrete and continuous time systems). The underlying philosophy behind their methods is apparently that if a flow is ergodic and the system observation has a sufficiently special value, the system is completely observable. In this paper we prove observability for observed systems whose underlying flow is minimal and distal. While our results hold also in discrete time, we illustrate this result for invariant ergodic systems on nilmanifolds, i.e. those invariant flows with an infinitesimal generator that is ‘irrational modulo the commutator’. One well-known example of such a flow is the irrational flow on a torus studied by Drager and Martin.