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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.

In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential equations of the form $${\left(r\left(t\right)\psi \left(x\left(t\right)\right){\left[x\left(t\right)+p\left(t\right)x\left(\tau \left(t\right)\right)\right]}^{\text{'}}\right)}^{\text{'}}+q\left(t\right)f\left(x\left[\sigma \left(t\right)\right]\right)=0$$ . Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0.