Sufficient conditions are presented for all bounded solutions of the linear system of delay differential equations $${(-1)}^{m+1}\frac{d^m{y}_i\left(t\right)}{d{t}^m}+\sum _{j=1}^n{q}_{ij}{y}_j(t-h_{jj})=0,m\ge 1,i=1,2,...,n,$$ to be oscillatory, where $q_{ij}\epsilon (-\infty ,\infty )$, $h_{jj}\in (0,\infty )$, $i,j=1,2,...,n$. Also, we study the oscillatory behavior of all bounded solutions of the linear system of neutral differential equations $${(-1)}^{m+1}\frac{d^m}{d{t}^m}(y_i\left(t\right)+c{y}_i(t-g))+\sum _{j=1}^n{q}_{ij}{y}_j(t-h)=0,$$ where $c$, $g$ and $h$ are real constants and $i=1,2,...,n$.

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].

The aim of this paper is to deduce oscillatory and asymptotic behavior of the solutions of the $n-$th order neutral differential equation $${(x\left(t\right)-px(t-\tau ))}^{\left(n\right)}-q\left(t\right)x\left(\sigma \left(t\right)\right)=0,$$ where $\sigma \left(t\right)$ is a delayed or advanced argument.