summary:We study oscillatory properties of solutions of systems \[ \begin{aligned} {[y_1(t)-a(t)y_1(g(t))]}^{\prime }=&p_1(t)y_2(t), y_2^{\prime }(t)=&{-p_2}(t)f(y_1(h(t))), \quad t\ge t_0. \end{aligned} \
summary:This paper deals with the second order nonlinear neutral differential inequalities (Aν): (−1)νx(t){z′′(t)+(−1)νq(t)f(x(h(t)))}≤0,t≥t0≥0, where ν=0 or ν=1,z(t)=x(t)+p(t)x(t−τ),0<τ= const, p,q,h:[t0,∞)→Rf:R→R are continuous functions. There are proved sufficient conditions under which every bounded solution of (Aν) is either oscillatory or $\ \liminf \limits _{t\rightarrow \infty }|x(t)|=0.