  We consider a polyharmonic operator $H=(-\Delta)^l+V(\x)$ in dimension two
with $l\geq 2$, $l$ being an integer, and a quasi-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 $e^{i< \k,\x>}$
at the high energy region. Second, the isoenergetic curves in the space of
momenta $\k$ corresponding to these eigenfunctions have a form of slightly
distorted circles with holes (Cantor type structure). A new method of
multiscale analysis in the momentum space is developed to prove these results.
