The paper gives some new oscillation criteria for all solutions of the \(n\)th order neutral differential equation \[ {d^n \over {dt^n}} (x(t)- P(t) x(t-\tau))+ Q(t) x(t-\sigma)=0 \] where \(P\in C([t_0,\infty), \mathbb{R})\), \(Q\in C([t_0,\infty), \mathbb{R}^+)\), \(\tau>0\), \(\sigma\geq 0\) and \(n\) is odd. The results obtained do not need the usual hypothesis \(\int^\infty_{t_0} s^{n-1} Q(s)ds=\infty\).