  Let $M$ be a compact connected Fujiki manifold, $G$ a semisimple affine
algebraic group over $\mathbb C$ with one simple factor and $P$ a fixed proper
parabolic subgroup of $G$. For a holomorphic principal $G$--bundle $E_G$ over
$M$, let ${\mathcal E}_P$ be the holomorphic principal $P$-bundle
$E_G\rightarrow E_G/P$ given by the quotient map. We prove that the following
three statements are equivalent: (1) ${\rm ad}(E_G)$ is numerically flat, (2)
the holomorphic line bundle $\bigwedge^{\rm top} {\rm ad}({\mathcal E}_P)^*$ is
nef, and (3) for every reduced irreducible compact complex analytic space $Z$
with a K\"ahler form $\omega$, holomorphic map $\gamma : Z \rightarrow M$, and
holomorphic reduction of structure group $E_P \subset \gamma^*E_G$ to $P$, the
inequality ${\rm degree}({\rm ad}(E_P)) \leq 0$ holds.
