We establish some new oscillation criteria for the second order neutral delay differential equation [r(t)|[x(t) + p(t)x[τ (t)]]′ | α−1 [x(t) + p(t)x[τ (t)]]′ ] ′ + q(t)f(x[σ(t)]) = 0. The obtained results supplement those of Dzurina and Stavroulakis, Sun and Meng, Xu and Meng, Baculíková and Lacková. We also make a slight improvement of one assumption in the paper of Xu and Meng.