This article, is concerned with finding sufficient conditions for the oscillatory and asymptotic behaviour of solutions of the higher order neutral delay differential equationwhere, n ≥ 2, is any positive integer,The functional delays r j (t) ≤ t for each j and g(t) ≤ t, h(t) ≤ t and all of them approach ∞ as t → ∞.The results hold when u ≡ 0 and f (t) ≡ 0. This paper extends, generalizes and improves some known results and answers an open problem.

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.