S. Gindikin and the author defined a
G
R
G_{\mathbb {R}}
-
K
C
K_{\mathbb {C}}
invariant subset
C
(
S
)
C(S)
of
G
C
G_{\mathbb {C}}
for each
K
C
K_{\mathbb {C}}
-orbit
S
S
on every flag manifold
G
C
/
P
G_{\mathbb {C}}/P
and conjectured that the connected component
C
(
S
)
0
C(S)_0
of the identity would be equal to the Akhiezer-Gindikin domain
D
D
if
S
S
is of nonholomorphic type. This conjecture was proved for closed
S
S
in the works of J. A. Wolf, R. Zierau, G. Fels, A. Huckleberry and the author. It was also proved for open
S
S
by the author. In this paper, we prove the conjecture for all the other orbits when
G
R
G_{\mathbb {R}}
is of non-Hermitian type.