Properties of quantum Nambu-brackets are studied in various physical situations. The brackets are shown to define time evolution in ways that can be quite novel, perhaps even very unusual, but which are nonetheless always fully consistent. The key physical ideas are to use different time scales on different invariant sectors of a system, and to
conjoin time evolution with symmetries of the system's dynamics. For finite times, this formulation of time-development is not the usual
unitary transformation, but nonetheless it gives results from which conventional, unitarily evolved data can be recovered. The methods are applicable to quantum field theory, perhaps the physical deas more generally than the Nambu brackets.