  The condition for a negative index of refraction with respect to the vacuum
index is established in terms of permittivity and permeability
susceptibilities. It is found that the imposition of analyticity to satisfy the
Kramers-Kronig relations is a sufficiently general criterion for a physical
negative index. The satisfaction of the Kramers-Kronig relations is a
manifestation of the principle of causality and the predicted frequency region
of negative index agrees with the Depine-Lakhtakia condition for the phase
velocity being anti-directed to the Poynting vector, although the conditions
presented here do not assume {\it a priori} a negative solution branch for n.
