By means of the averaging technique and the generalized Riccati transformation technique, we establish some oscillation criteria for the second-order quasilinear neutral delay dynamic equations [ r ( t ) | x Δ ( t ) | γ - 1 x Δ ( t ) ] Δ + q 1 ( t ) | y ( δ 1 ( t ) ) | α - 1 y ( δ 1 ( t ) ) + q 2 ( t ) | y ( δ 2 ( t ) ) | β - 1 y ( δ 2 ( t ) ) = 0 , t ∈ [ t 0 , ∞ ) 𝕋 , where x ( t ) = y ( t ) + p ( t ) y ( τ ( t ) ) , and the time scale interval is [ t 0 , ∞ ) 𝕋 : = [ t 0 , ∞ ) ∩ 𝕋 . Our results in this paper not only extend the results given by Agarwal et al. (2005) but also unify the oscillation of the second-order neutral delay differential equations and the second-order neutral delay difference equations.