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In this paper we consider the equation $$y^{\text{'}\text{'}\text{'}}+q\left(t\right){y^{\text{'}}}^{\alpha }+p\left(t\right)h\left(y\right)=0,$$ where $p,q$ are real valued continuous functions on $[0,\infty )$ such that $q\left(t\right)\ge 0$, $p\left(t\right)\ge 0$ and $h\left(y\right)$ is continuous in $(-\infty ,\infty )$ such that $h\left(y\right)y>0$ for $y\ne 0$. We obtain sufficient conditions for solutions of the considered equation to be nonoscillatory. Furthermore, the asymptotic behaviour of these nonoscillatory solutions is studied.

In this paper we are concerned with the oscillation of third order nonlinear delay differential equations of the form $${\left(r_2\left(t\right){\left(r_1\left(t\right)x^{\text{'}}\right)}^{\text{'}}\right)}^{\text{'}}+p\left(t\right)x^{\text{'}}+q\left(t\right)f\left(x\left(g\left(t\right)\right)\right)=0.$$ We establish some new sufficient conditions which insure that every solution of this equation either oscillates or converges to zero.