Let G / P be a rational homogeneous variety, where P is a parabolic subgroup of a simple and simply connected linear algebraic group G defined over an algebraically closed field of characteristic zero. A homogeneous principal bundle over G / P is semistable (respectively, polystable) if and only if it is equivariantly semistable (respectively, equivariantly polystable). A stable homogeneous principal H -bundle ( E H , ρ ) is equivariantly stable, but the converse is not true in general. If a homogeneous principal H -bundle ( E H , ρ ) is equivariantly stable, but the principal H -bundle E H is not stable, then the principal H -bundle E H admits an action ρ ′ of G such that the pair ( E H , ρ ′) is a homogeneous principal H -bundle which is not equivariantly stable.