  The critical fluctuations in a mesoscopic superconducting ring are studied
within the Ginzburg-Landau approach. The nonlocal conductivity as well as the
specific heat are calculated as functions of the magnetic flux $\Phi$ through
the ring. At $\Phi=\Phi_0/2$ two low-energy eigenstates become degenerate and
near this point the behavior of fluctuations-dependent quantities change
dramatically: both the zero Fourier component $\sigma_0$ of the fluctuation
conductivity and the specific heat become non-monotonic functions of
$|\Phi-\Phi_0/2|$ with rather special resonant structure.
