  The stability of 5-D brane-world models under conformal perturbations is
investigated. The analysis is carried out in the general case and then it is
applied to particular solutions. It is shown that models with the Poincare and
the de Sitter branes are unstable because they have negative mass squared of
gravexcitons whereas models with the Anti de Sitter branes have positive
gravexciton mass squared and are stable. It is also shown that 4-D effective
cosmological and gravitational constants on branes as well as gravexciton
masses undergo hierarchy: they have different values on different branes.
