  A ballean (or coarse structure) is a set endowed with some family of subsets,
the balls, is such a way that balleans with corresponding morphisms can be
considered as asymptotic counterparts of uniform topological spaces. For a
ballean $\mathcal{B}$ on a set $X$, the hyperballean $\mathcal{B}^{\flat}$ is a
ballean naturally defined on the set $X^{\flat}$ of all bounded subsets of $X$.
We describe all balleans with hyperballeans of bounded geometry and analyze the
structure of these hyperballeans.
