The author studies the second order neutral differential difference equation \[ \quad u''(t)-cx''(t-r)+px[g(t)]=0,\quad x''(t)-cx''(t- r)+p(t)x[g(t)]=0, \] where \(r>0\), \(p>0\), \(p(t)>0\), \(1>c\geq 0\), g(t)\(\leq t\), \(\lim_{t\to +\infty}g(t)=+\infty\). He gives some types of nonoscillatory solutions which satisfy \(x(t)[x(t)-cx(t-r)]>0\) and some sufficient conditions under which there exists one of these nonoscillatory solutions.