  We study nonlinear gravitational perturbations of vacuum Einstein equations,
with $\Lambda<0$ in $(n+2)$ dimensions, with $n>2$, generalizing previous
studies for $n=2$. We follow the formalism by Ishibashi, Kodama and Seto to
decompose the metric perturbations into tensor, vector and scalar sectors, and
simplify the Einstein equations. The tensor perturbations are the new feature
of higher dimensions. We render the metric perturbations asymptotically anti-de
Sitter by employing a suitable gauge choice for each of the sectors. Finally,
we analyze the resonant structure of the perturbed equations at second order
for the five dimensional case, by a partial study of single mode tensor-type
perturbations at the linear level. For the cases we studied, resonant terms
vanish at second order.
