Summary: Some sufficient conditions are established for the oscillation of second-order neutral differential equations
where and . On the other hand, some new oscillation criteria are established for the second-order nonlinear neutral delay differential equations
where . The results obtained here complement and correct some known results by L. Ye and Z. Xu [Appl. Math. Comput. 207, No. 2, 388–396 (2009; Zbl 1168.34346)]. Some examples are given to illustrate the main results.