  A positive integer $m$ will be called a {\it finitistic order} for an element
$\gamma$ of a group $\Gamma$ if there exist a finite group $G$ and a
homomorphism $h:\Gamma\to G$ such that $h(\gamma)$ has order $m$ in $G$. It is
shown that up to conjugacy, all but finitely many elements of a given finitely
generated, torsion-free Kleinian group admit a given integer $m>2$ as a
finitistic order.
