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The authors study the n-th order nonlinear neutral differential equations with the quasi – derivatives $L_n[x\left(t\right)+{(-1)}^{r}P\left(t\right)x\left(g\left(t\right)\right)]+\delta Q\left(t\right)f\left(x\left(h\left(t\right)\right)\right)=0,$ where $n\ge 2,r\in \{1,2\},$ and $\delta =\pm 1.$ There are given sufficient conditions for solutions to be either oscillatory or they converge to zero.