We establish some new oscillation criteria for the second-order quasilinear neutral delay dynamic equations [ r ( t ) ( z Δ ( t ) ) γ ] Δ + q 1 ( t ) x α ( τ 1 ( t ) ) + q 2 ( t ) x β ( τ 2 ( t ) ) = 0 on a time scale 𝕋 , where z ( t ) = x ( t ) + p ( t ) x ( τ 0 ( t ) ) , 0 < α < γ < β . Our results generalize and improve some known results for oscillation of second-order nonlinear delay dynamic equations on time scales. Some examples are considered to illustrate our main results.