  We consider principal bundles over homogeneous spaces G/P, where P is a
parabolic subgroup of a semisimple and simply connected complex linear
algebraic group G. We prove that a holomorphic principal H--bundle, where H is
a complex reductive group, is homogeneous if the adjoint vector bundle ad(E) is
homogeneous. We also show that E is homogeneous if its associated vector bundle
for any finite dimensional faithful H--module is homogeneous.
