  We study the complex part of the spectrum of the the Gurtin-Pipkin
integral-differential equation of the second order in time. We consider the
model case when the kernel is a sum of exponentials $a_k\exp(-b_k)$ with
$a_k=1/k^\a$, $b_k=k^\b$. We show that there are two complex sequences of
points of the spectrum asymptotically close to the spectrum points of the wave
equation.
