Some new oscillation criteria for the second-order neutral delay differential equation ( r ( t ) z ′ ( t ) ) ′ + q ( t ) x ( σ ( t ) ) = 0 , t ≥ t 0 are established, where ∫ t 0 ∞ ( 1 / r ( t ) ) d t = ∞ , z ( t ) = x ( t ) + p ( t ) x ( τ ( t ) ) , 0 ≤ p ( t ) ≤ p 0 < ∞ , q ( t ) > 0 . These oscillation criteria extend and improve some known results. An example is considered to illustrate the main results.