  Inhomogeneous small-amplitude plane waves of (complex) frequency $\omega$ are
propagated through a linear dissipative material which displays hereditary
viscoelasticity. The energy density, energy flux and dissipation are quadratic
in the small quantities, namely, the displacement gradient, velocity and
velocity gradient, each harmonic with frequency $\omega$, and so give rise to
attenuated constant terms as well as to inhomogeneous plane waves of frequency
$2\omega$. The quadratic terms are usually removed by time averaging but we
retain them here as they are of comparable magnitude with the time-averaged
quantities of frequency $\omega$. A new relationship is derived in hereditary
viscoelasticity that connects the amplitudes of the terms of the energy
density, energy flux and dissipation that have frequency $2\omega$. It is shown
that the complex group velocity is related to the amplitudes of the terms with
frequency $2\omega$ rather than to the attenuated constant terms as it is for
homogeneous waves in conservative materials.
