  We study the dependence of the eigenvalues of the biharmonic operator subject
to Neumann boundary conditions on the Poisson's ratio. In particular, we prove
that the Neumann eigenvalues are Lipschitz continuous with respect to
$\sigma\in [0,1[$ and that all the Neumann eigenvalues tend to zero as
$\sigma\rightarrow 1^-$. Moreover, we show that the Neumann problem defined by
setting $\sigma=1$ admits a sequence of positive eigenvalues of finite
multiplicity which are not limiting points for the Neumann eigenvalues with
$\sigma\in[0,1[$ as $\sigma\rightarrow 1^-$, and which coincide with the
Dirichlet eigenvalues of the biharmonic operator.
