  A continuous map $f$ on a compact metric space $X$ induces in a natural way
the map $\tilde f$ on the hyperspace $\mathcal K(X)$ of all closed non-empty
subsets of $X$. We study the question of transmission of chaos between $f$ and
$\tilde f$. We deal with generic, generic $\varepsilon$-, dense and dense
$\varepsilon$-chaos for interval maps. We prove that all four types of chaos
transmit from $f$ to $\tilde f$, while the converse transmission from $\tilde
f$ to $f$ is true for generic, generic $\varepsilon$- and dense
$\varepsilon$-chaos. Moreover, the transmission of dense $\varepsilon$- and
generic $\varepsilon$-chaos from $\tilde f$ to $f$ is true for maps on general
compact metric spaces.
