  Dynamical systems can be quantised only if they are Hamiltonian. This prompts
the question from which our talk gets its title. We show how the simple
predator-prey equation and the damped harmonic oscillator can be considered to
be Hamiltonian with respect to an infinite number of non-standard Poisson
brackets. This raises some interesting questions about the nature of
quantisation. Questions which are valid even for flows which possess a
canonical structure.
