The behavior of backward waves is considered from a purely wave propagation point of view. Beginning with the condition that the phase and group velocity vectors are anti-parallel a form for the index of refraction is derived which results in backwards wave behavior at all frequencies. The dispersion relation for this index is found and it is shown that, for the case considered, this index is necessarily negative. The requirement for backwards wave behavior -that the phase and group velocity are "perfectly" anti-parallel - is then relaxed and the situation is considered where these two velocity vectors have one or two anti-parallel components (the angle between them is between 90° and 270°). It is shown that this implies propagation through an anisotropic medium and that backwards wave behavior can still occur if at least one of the axes exhibits a negative index. This phenomenon, however, is not restricted to the propagation along the negative index axes.
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