Let X be an arbitrary reflexive Banach space, and let
N
\mathcal {N}
be a nest on X. Denote by
D
(
N
)
\mathcal {D}(\mathcal {N})
the set of all derivations from
Alg
N
\operatorname {Alg}\mathcal {N}
into
Alg
N
\operatorname {Alg}\mathcal {N}
. For
N
⊂
N
N \subset \mathcal {N}
, we set
N
−
=
∨
{
M
∈
N
:
M
⊂
N
}
{N_ - } = \vee \{ M \in \mathcal {N}:M \subset N\}
. We also write
0
−
=
0
{0_ - } = 0
. Finally, for
E
,
F
∈
N
E, F \in \mathcal {N}
define
(
E
,
F
]
=
{
K
∈
N
:
E
⊂
K
⊆
F
}
(E,F] = \{ K \in \mathcal {N}:E \subset K \subseteq F\}
. In this paper we prove that a sufficient condition for
D
(
N
)
\mathcal {D}(\mathcal {N})
to be (topologically) algebraically reflexive is that for all
0
≠
E
∈
N
0 \ne E \in \mathcal {N}
and for all
X
≠
F
∈
N
X \ne F \in \mathcal {N}
, there exist
M
∈
(
0
,
E
]
M \in (0,E]
and
N
∈
(
F
,
X
]
N \in (F,X]
, such that
M
−
⊂
M
{M_ - } \subset M
and
N
−
⊂
N
{N_ - } \subset N
. In particular, we prove that this condition automatically holds for nests acting on finite-dimensional Banach spaces.