  As is well-known, asymptotically flat, static and spherically symmetric black
holes do not admit stable bound orbits of massive/massless particles outside
the horizon in higher-dimensional Einstein gravity. However, for massive
particles, this dramatically changes in higher curvature theories. We clarify
the parameter range such that there exist stable bound orbits in
$d$-dimensional Einstein-Gauss-Bonnet theories for $6\leq d\leq 9$. In
particular, we show the existence of the lower bound of the Gauss-Bonnet
coupling constant below which stable bound orbits cease to exist. Moreover, we
also find that for AdS-black holes in the theories, there can exist two stable
circular orbits outside the horizon.
