  We study the stability of static black holes in Lovelock theory which is a
natural higher dimensional generalization of Einstein theory. We show that
Lovelock black holes are stable under vector perturbations in all dimensions.
However, we prove that small Lovelock black holes are unstable under tensor
perturbations in even-dimensions and under scalar perturbations in
odd-dimensions. Therefore, we can conclude that small Lovelock black holes are
unstable in any dimensions. The instability is stronger on small scales and
hence catastrophic in the sense that there is no smooth descendant.
