  We study the question of whether oscillations between non-relativistic
neutrinos or between relativistic and non-relativistic neutrinos are possible.
The issues of neutrino production and propagation coherence and their impact on
the above question are discussed in detail. It is demonstrated that no neutrino
oscillations can occur when neutrinos that are non-relativistic in the
laboratory frame are involved, except in a strongly mass-degenerate case. We
also discuss how this analysis depends on the choice of the Lorentz frame. Our
results are for the most part in agreement with Hinchliffe's rule.
