Asymptotic behavior of solutions of neutral nonlinear differential equations

summary:In this paper we study asymptotic behavior of solutions of second order neutral functional differential equation of the form \[ \Big (x(t)+px(t-\tau )\Big )^{\prime \prime }+f(t,x(t))=0\,. \] We present conditions under which all nonoscillatory solutions are asymptotic to $at+b$ as $t\rightarrow \infty $, with $a,b\in R$. The obtained results extend those that are known for equation \[ u^{\prime \prime }+f(t,u)=0\,. \