  We prove the instability of the gravitating regular sphaleron solutions of
the $SU(2)$ Einstein-Yang-Mills-Higgs system with a Higgs doublet, by studying
the frequency spectrum of a class of radial perturbations. With the help of a
variational principle we show that there exist always unstable modes. Our
method has the advantage that no detailed knowledge of the equilibrium solution
is required. It does, however, not directly apply to black holes.
