  Eleven-dimensional supergravity admits non-supersymmetric solutions of the
form AdS(5)xM(6) where M(6) is a positive Kahler-Einstein space. We show that
the necessary and sufficient condition for such solutions to be stable against
linearized bosonic supergravity perturbations can be expressed as a condition
on the spectrum of the Laplacian acting on (1,1)-forms on M(6). For M(6)=CP(3),
this condition is satisfied, although there are scalars saturating the
Breitenlohner-Freedman bound. If M(6) is a product S(2)xM(4) (where M(4) is
Kahler-Einstein) then there is an instability if M(4) has a continuous
isometry. We show that a potential non-perturbative instability due to 5-brane
nucleation does not occur. The bosonic Kaluza-Klein spectrum is determined in
terms of eigenvalues of operators on M(6).
