We study oscillatory properties of solutions of the Emden-Fowler type differential equation $$u^{(n)}(t)+p(t)\big |u(\sigma (t))\big |^\lambda \operatorname{sign} u(\sigma (t))=0,$$ where $0<\lambda <1$, $p\in L_{\rm loc }(\Bbb R_+;\Bbb R)$, $\sigma \in C(\Bbb R_+;\Bbb R_+)$ and $\sigma (t)\ge t$ for $t\in \Bbb R_+$. \endgraf Sufficient (necessary and sufficient) conditions of new type for oscillation of solutions of the above equation are established. \endgraf Some results given in this paper generalize the results obtained in the paper by Kiguradze and Stavroulakis (1998).