  We investigate the evolution of small perturbations around black strings and
branes which are low energy solutions of string theory. For simplicity we focus
attention on the zero charge case and show that there are unstable modes for a
range of time frequency and wavelength in the extra $10-D$ dimensions. These
perturbations can be stabililized if the extra dimensions are compactified to a
scale smaller than the minimum wavelength for which instability occurs and thus
will not affect large astrophysical black holes in four dimensions. We comment
on the implications of this result for the Cosmic Censorship Hypothesis.
