By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria and study the asymptotic behavior of the nonoscillatory solutions of the second-order nonlinear neutral delay dynamic equation $$ [r(t)[y(t) + p(t)y(\tau (t))]^\Delta ]^\Delta + q(t)f(y(\delta (t))) = 0 $$ , on a time scale $$ \mathbb{T} $$ . The results improve some oscillation results for neutral delay dynamic equations and in the special case when $$ \mathbb{T} $$ = ℝ our results cover and improve the oscillation results for second-order neutral delay differential equations established by Li and Liu [Canad. J. Math., 48 (1996), 871–886]. When $$ \mathbb{T} $$ = ℕ, our results cover and improve the oscillation results for second order neutral delay difference equations established by Li and Yeh [Comp. Math. Appl., 36 (1998), 123–132]. When $$ \mathbb{T} $$ =hℕ, $$ \mathbb{T} $$ = {t: t = q k , k ∈ ℕ, q > 1}, $$ \mathbb{T} $$ = ℕ2 = {t 2: t ∈ ℕ}, $$ \mathbb{T} $$ = $$ \mathbb{T}_n $$ = {t n = Σ k=1 n $$ \tfrac{1} {k} $$ , n ∈ ℕ0}, $$ \mathbb{T} $$ ={t 2: t ∈ ℕ}, $$ \mathbb{T} $$ = {√n: n ∈ ℕ0} and $$ \mathbb{T} $$ ={ $$ \sqrt[3]{n} $$ : n ∈ ℕ0} our results are essentially new. Some examples illustrating our main results are given.