  We consider magnetic oscillations of resistivity of a clean hollow cylinder
with fluctuating radius $R$, threaded by magnetic flux $\Phi$. We demonstrate,
that for very weak fluctuations $\Delta R\ll p_F^{-1}$ the oscillations have a
standard period $2\Phi_0$ (where $\Phi_0=\pi c\hbar/2e$), characteristic for
oscillations in a clean system, while for $\Delta R\gg p_F^{-1}$ they become
$\Phi_0$-periodic, which was expected only for dirty systems with $R\gg l$. The
work is motivated by observation of predominantly $\Phi_0$-periodic magnetic
oscillations in very clean Bismuth wires.
