  We show that negative refraction in materials can occur at frequencies
$\omega$ where the real parts of the permittivity $\veps(\omega)$ and the
permeability $\mu(\omega)$ have different sign, and that light with such
frequencies can propagate just as well as light with frequencies where they
have equal sign. Therefore, for negative refraction one does not need to be in
the ``double-negative'' regime. We consider negative refractive index achiral
materials using the Drude-Lorentz model and chiral materials using the
Drude-Born-Fedorov model. We find that the time-averaged Poynting vector always
points along the wave vector, the time-averaged energy-flux density is always
positive, and the time-averaged energy density is positive (negative) when the
refractive index is positive (negative). The phase velocity is negative when
the real part of the refractive index is negative, and the group velocity
generally changes sign several times as a function of frequency near resonance.
