We study oscillatory properties of solutions of systems $$\begin{array}{ccc}\hfill {[y_1\left(t\right)-a\left(t\right)y_1\left(g\left(t\right)\right)]}^{\text{'}}=& p_1\left(t\right)y_2\left(t\right),y_2^{\text{'}}\left(t\right)=\hfill & \hfill -p_2\left(t\right)f\left(y_1\left(h\left(t\right)\right)\right),t\ge t_0.\end{array}$$

Oscillation and nonoscillation criteria are established for the equation $$u^{\text{'}\text{'}}+{p\left(t\right)\left|u\right|}^{\alpha }{\left|u^{\text{'}}\right|}^{1-\alpha }sgnu=0,$$ where $\alpha \in ]0,1]$, and $p:[0,+\infty [\to [0,+\infty [$ is a locally summable function.

In the paper the fourth order nonlinear differential equation $y^{\left(4\right)}+{\left(q\left(t\right)y^{\text{'}}\right)}^{\text{'}}+r\left(t\right)f\left(y\right)=0$, where $q\in C^1\left([0,\infty )\right)$, $r\in C^0\left([0,\infty )\right)$, $f\in C^0\left(R\right)$, $r\ge 0$ and $f\left(x\right)x>0$ for $x\ne 0$ is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for $t\to \infty$.