  In this paper we investigate the operator
$H_{\beta}=-\Delta-\beta\delta(\cdot-\Gamma)$ in $L^{2}({\Bbb R}^{2})$, where
$\beta>0$ and $\Gamma$ is a closed $C^{4}$ Jordan curve in ${\Bbb R}^{2}$. We
obtain the asymptotic form of each eigenvalue of $H_{\beta}$ as $\beta$ tends
to infinity. We also get the asymptotic form of the number of negative
eigenvalues of $H_{\beta}$ in the strong coupling asymptotic regime.
