Sufficient conditions are obtained for oscillation of all solutions of a class of forced nth order linear and nonlinear neutral delay differential equations. Also, asymptotic behaviour of nonoscillatory solutions of a class of forced first order neutral equations is studied.

Oscillation and nonoscillation criteria for the self-adjoint linear differential equation $${\left(t^{\alpha }{y}^{\text{'}\text{'}}\right)}^{\text{'}\text{'}}-\frac{{\gamma }_{2,\alpha }}{t^{4-\alpha }}y=q\left(t\right)y,\alpha \notin \{1,3\},$$ where $${\gamma }_{2,\alpha }=\frac{{(\alpha -1)}^2{(\alpha -3)}^2}{16}$$ and $q$ is a real and continuous function, are established. It is proved, using these criteria, that the equation $${\left(t^{\alpha }{y}^{\text{'}\text{'}}\right)}^{\text{'}\text{'}}-\left(\frac{{\gamma }_{2,\alpha }}{t^{4-\alpha }}+\frac{\gamma }{t^{4-\alpha }{ln}^{2}t}\right)y=0$$ is nonoscillatory if and only if $\gamma \le \frac{{\alpha }^2-4\alpha +5}{8}$.

This paper deals with the second order nonlinear neutral differential inequalities $\left(A_{\nu }\right)$: ${(-1)}^{\nu }x\left(t\right)\{z^{\text{'}\text{'}}\left(t\right)+{(-1)}^{\nu }q\left(t\right)f\left(x\left(h\left(t\right)\right)\right)\}\le 0,$$t\ge t_0\ge 0...$

A sufficient condition for the nonoscillation of nonlinear systems of differential equations whose left-hand sides are given by $n$-th order differential operators which are composed of special nonlinear differential operators of the first order is established. Sufficient conditions for the oscillation of systems of two nonlinear second order differential equations are also presented.

The purpose of this paper is to obtain oscillation criterions for the differential system of neutral type.