  We consider a polyharmonic operator $H=(-\Delta)^l+V(x)$ in dimension two
with $l\geq 6$ and a limit-periodic potential $V(x)$. We prove that the
spectrum of $H$ contains a semiaxis and there is a family of generalized
eigenfunctions at every point of this semiaxis with the following properties.
First, the eigenfunctions are close to plane waves $e^{i< \vec k,\vec x>}$ at
the high energy region. Second, the isoenergetic curves in the space of momenta
$\vec k$ corresponding to these eigenfunctions have a form of slightly
distorted circles with holes (Cantor type structure).
