  We give a Miyaoka-type semistability criterion for principal Higgs G-bundles
E on complex projective manifolds of any dimension, i.e., we prove that E is
semistable and the second Chern class of its adjoint bundle vanishes if and
only if certain line bundles, obtained from the characters of the parabolic
subgroups of G, are numerically effective. We also give alternative
characterizations in terms of a notion of numerical effectiveness of Higgs
vector bundles we have recently introduced.
