  Let $\Omega$ be an annulus. We prove that the mean field equation
$-\Delta\psi=\frac{e\sp{-\beta\psi}}{\int\sb{\Omega}e\sp{-\beta\psi}} $ admits
a solution with zero boundary for $\beta\in (-16\pi,-8\pi)$. This is a
supercritical case for the Moser-Trudinger inequality.
