We discuss the problem presented by S. R. Bernfeld and J. R. Haddock in the international conference “Nonlinear systems and applications” (1976). We investigate the existence, uniqueness, boundedness and asymptotic behavior of the solutions of functional differential equations \(dx/dt=f(x)+G(x^ J_ t),\) where \(x^ T_ t(\theta)=x_ t(\theta)\), \(\theta\in [-r,-s]\), \(s>0\).