  We develop a covariant scheme to describe the dynamics of small perturbations
on Lovelock type extended objects propagating in a flat Minkowski spacetime.
The higher-dimensional analogue of the Jacobi equation in this theory becomes a
wave type equation for a scalar field $\Phi$. Whithin this framework, we
analyse the stability of membranes with a de Sitter geometry where we find that
the Jacobi equation specializes to a Klein-Gordon (KG) equation for $\Phi$
possessing a tachyonic mass. This shows that, to some extent, these type of
extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action
which is by no means coincidental because the DNG model is the simplest
included in this type of gravity.
