  Let $G_R$ be a classical real direct limit Lie group and $g_R$ its Lie
algebra. The parabolic subalgebras of the complexification $g_C$ were described
by the first two authors. In the present paper we extend these results to
$g_R$. This also gives a description of the parabolic subgroups of $G_R$.
Furthermore, we give a geometric criterion for a parabolic subgroup $P_C$ of
$G_C$ to intersect $G_R$ in a parabolic subgroup. This criterion involves the
$G_R$-orbit structure of the flag ind-manifold $G_C/P_C$.
