  Spectral analysis of operator-functions which are the symbols of the abstract
integrodifferential equations of the Gurtin-Pipkin is provided. These equations
represent abstract wave equations disturbed by terms involving Volterra
operators. Correct solvability in the Sobolev space $W_{2}^{2}((0, T), A^2)$,
for arbitrary $T>0$, of that abstract integrodifferential equations is also
studied.
