In the paper, we combine new generalization of classical Philos and Staikos lemma together with suitable comparison technique to offer new oscillation criteria for \(n\)-th order neutral delay differential equation $$\begin{aligned} \Big (r(t)\left[ z'(t)\right] ^{\gamma }\Big )^{(n-1)} +q(t)x^{\gamma }(\sigma (t))=0. \end{aligned}$$ The presented technique essentially simplifies the examination of the higher order differential equations.