For a Banach space
X
X
defined in terms of a big-
O
O
condition and its subspace x defined by the corresponding little-
o
o
condition, the biduality property (generalizing the concept of reflexivity) asserts that the bidual of x is naturally isometrically isomorphic to
X
X
. The property is known for pairs of many classical function spaces (such as
(
ℓ
∞
,
c
0
)
(\ell _\infty , c_0)
, (BMO, VMO), (Lip, lip), etc.) and plays an important role in the study of their geometric structure. The present paper is devoted to the biduality property for traces to closed subsets
S
⊂
R
n
S\subset \mathbb {R}^n
of a generalized Zygmund space
Z
ω
(
R
n
)
Z^\omega (\mathbb {R}^n)
. The method of the proof is based on a careful analysis of the structure of geometric preduals of the trace spaces along with a powerful finiteness theorem for the trace spaces
Z
ω
(
R
n
)
|
S
Z^\omega (\mathbb {R}^n)|_S
.