In this paper we consider the equation \[y^{\prime \prime \prime} + q(t){y^{\prime }}^{\alpha} + p(t) h(y) =0,\] where $p,q$ are real valued continuous functions on $[0,\infty)$ such that $q(t) \ge 0$, $p(t) \ge 0$ and $h(y)$ is continuous in $(-\infty ,\infty)$ such that $h(y)y>0$ 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.