The authors consider the scalar neutral functional differential equation \[ {d\over dt} \Biggl[ x(t)- \int^{- r_ 0}_{- r} x(t+ s) d\nu(s)\Biggr]= f(x_ t), \] where \(\nu: [- r, - r_ 0]\to \mathbb{R}\) is nondecreasing and \(\nu(- r_ 0)- \nu(- r)< 1\), \(f: C([- r; 0]; \mathbb{R})\to \mathbb{R}\) is locally Lipschitz continuous and \(x_ t(\cdot)\in C([- r; 0]; \mathbb{R})\), \(x_ t(s)= x(t+ s)\) for \(s\in [- r; 0]\).
Using a certain ordering of the space \(C([- r; 0]; \mathbb{R})\), some general sufficient conditions guaranteeing the strong order preserving property of the solution semiflow are obtained.