An
n
n
th order, possibly nonselfadjoint, ordinary differential expression
L
L
is said to be in the limit point condition if the maximal operator
L
M
{L_M}
in
L
2
[
0
,
∞
)
{L_2}[0,\infty )
is an
n
n
-dimensional extension of the minimal operator
L
0
{L_0}
. If range
L
0
{L_0}
is closed, this definition is equivalent to the assertion that nullity
L
M
+
nullity
(
L
+
)
M
=
n
{L_M} + \text {nullity} {({L^ + })_M} = n
, where
L
+
{L^ + }
is the formal adjoint of
L
L
. It also implies that any operator
T
T
such that
L
0
⊆
T
⊆
L
M
{L_0} \subseteq T \subseteq {L_M}
is the restriction of
L
M
{L_M}
to a set of functions described by a boundary condition at zero. In this paper, we discuss the question of when differential expressions involving complex polynomials in selfadjoint expressions are in the limit point condition.