  In the present paper we establish that the space $\exp_\beta X$ of compact
subsets of a Tychonoff space $X$ is superparacompact iff $X$ is so. Further, we
prove the Tychonoff map $\exp_{\beta} f:\ \exp_{\beta} X\rightarrow
\exp_{\beta} Y$ is superparacompact iff a given map $f:\ X\rightarrow Y$ is
superparacompact.
