  Let $M$ be a compact connected special flat affine manifold without boundary
equipped with a Gauduchon metric $g$ and a covariant constant volume form. Let
$G$ be either a connected reductive complex linear algebraic group or the real
locus of a split real form of a complex reductive group. We prove that a flat
principal $G$-bundle $E_G$ over $M$ admits a Hermitian-Einstein structure if
and only if $E_G$ is polystable. A polystable flat principal $G$--bundle over
$M$ admits a unique Hermitian-Einstein connection. We also prove the existence
and uniqueness of a Harder-Narasimhan filtration for flat vector bundles over
$M$.
