In this paper, the oscillation criteria for solutions of the neutral delay differential equation (NDDE) $${\left(y\left(t\right)-p\left(t\right)y\left(t-\tau \right)\right)}^{\left(n\right)}+\alpha Q\left(t\right)G\left(y\left(t-\sigma \right)\right)=f\left(t\right)$$ has been studied where $p\left(t\right)=1$ or $p\left(t\right)\le 0$, $\alpha =\pm 1$, $Q\in C\left([0,\infty ),R^{+}\right)$, $f\in C\left(\right[0,\infty ),R)$, $G\in C(R,R)$. This work improves and generalizes some recent results and answer some questions that are raised in [1].

Integral criteria are established for $dim{V}_i\left(p\right)=0$ and $dim{V}_i\left(p\right)=1,i\in \{0,1\}$, where $V_i\left(p\right)$ is the space of solutions $u$ of the equation $$u^{\text{'}\text{'}}+p\left(t\right)u=0$$ satisfying the condition $${\int }^{+\infty }\frac{u^2\left(s\right)}{s^i}ds<+\infty .$$