AbstractIn this work, we study the oscillatory behavior of even-order neutral delay differential equations $\upsilon ^{n}(l)+b(l)u(\eta (l))=0$
υ
n
(
l
)
+
b
(
l
)
u
(
η
(
l
)
)
=
0
, where $l\geq l_{0}$
l
≥
l
0
, $n\geq 4$
n
≥
4
is an even integer and $\upsilon =u+a ( u\circ \mu ) $
υ
=
u
+
a
(
u
∘
μ
)
. By deducing a new iterative relationship between the solution and the corresponding function, new oscillation criteria are established that improve those reported in (T. Li, Yu.V. Rogovchenko in Appl. Math. Lett. 61:35–41, 2016).