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We are interested in comparing the oscillatory and asymptotic properties of the equations $L_n[x\left(t\right)-P\left(t\right)x\left(g\left(t\right)\right)]+\delta f(t,x\left(h\left(t\right)\right))=0$ with those of the equations $M_n[x\left(t\right)-P\left(t\right)x\left(g\left(t\right)\right)]+\delta Q\left(t\right)q\left(x\left(r\left(t\right)\right)\right)=0.$

The work deals with non-Markov processes and the construction of systems of differential equations with delay that describe the probability vectors of such processes. The generating stochastic operator and properties of stochastic operators are used to construct systems that define non-Markov processes.

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.