  The spectrum of a selfadjoint quadratic operator pencil of the form
$\lambda^2M-\lambda G-A$ is investigated where $M\geq 0$, $G\geq 0$ are bounded
operators and $A$ is selfadjoint bounded below is investigated. It is shown
that in the case of rank one operator $G$ the eigenvalues of such a pencil are
of two types. The eigenvalues of one of these types are independent of the
operator $G$. Location of the eigenvalues of both types is described. Examples
for the case of the Sturm-Liouville operators $A$ are given.
