  In [GM1], we defined a G_R-K_C invariant subset C(S) of G_C for each
K_C-orbit S on every flag manifold G_C/P and conjectured that the connected
component C(S)_0 of the identity would be equal to the Akhiezer-Gindikin domain
D if S is of nonholomorphic type by computing many examples. In this paper, we
first prove (in Theorem 1.3 and Corollary 1.4) this conjecture for the open
K_C-orbit S on an ``arbitrary'' flag manifold generalizing the result of
Barchini. This conjecture for closed S was solved in [WZ1], [WZ2] (Hermitian
cases) and [FH] (non-Hermitian cases). We also deduce an alternative proof of
this result for non-Hermitian cases from Theorem 1.3.
