In this paper we prove the following form of the Phragmen-Brouwer Theorem: a locally connected, connected normal
T
1
{T_1}
-space
X
X
is unicoherent if and only if for every pair of disjoint nonseparating continua
C
C
and
D
D
in
X
X
,
C
∪
D
C \cup D
does not separate
X
X
. Among the several corollaries is the proposition:
X
X
is multicoherent if and only if
X
X
is the union of a circular chain of continua
{
A
0
,
A
1
,
A
2
,
A
3
}
\left \{ {{A_0},{A_1},{A_2},{A_3}} \right \}
where no three of the
A
i
{A_i}
’s have a point in common.