The purpose of this paper is to investigate some properties of the hyperspace $(\exp X,\tau_{lf})$, with the locally finite topology, when the space $(X,\tau)$ is a normal space and every closed countably compact subset of $X$ is compact (\emph{isc}-space). Some properties of \emph{isc}-spaces and \emph{iscc}-spaces are given. If $(X,\tau)$ is a normal \emph{isc}-space, then the space $\mathcal Z(X)=\{F\in X:F\text{ is compact}\}$ is a closed subspace of $(\exp X,\tau_{lf})$. Applications to paracom-pactness are given.