  We explore via linearized perturbation theory the Gregory-Laflamme
instability of the black string solutions of Einstein's equations with negative
cosmological constant recently discussed in literature. Our results indicate
that the black strings whose conformal infinity is the product of time and
$S^{d-3}\times S^1$ are stable for large enough values of the event horizon
radius. All topological black strings are also classically stable. We argue
that this provides an explicit realization of the Gubser-Mitra conjecture.
