  We study monotone skew-product semiflows generated by families of
nonautonomous neutral functional differential equations with infinite delay and
stable D-operator, when the exponential ordering is considered. Under adequate
hypotheses of stability for the order on bounded sets, we show that the
omega-limit sets are copies of the base to explain the long-term behavior of
the trajectories. The application to the study of the amount of material within
the compartments of a neutral compartmental system with infinite delay, shows
the improvement with respect to the standard ordering.
