The exponential ordering is exploited in the context of nonautonomous delay
systems, inducing monotone skew-product semiflows under less restrictive conditions
than usual. Some dynamical concepts linked to the order, such as semiequilibria, are
considered for the exponential ordering, with implications for the determination of
the presence of uniform persistence or the existence of global attractors. Also, some
important conclusions on the long-term dynamics and attraction are obtained for
monotone and sublinear delay systems for this ordering. The results are then applied
to almost periodic Nicholson systems and new conditions are given for the existence
of a unique almost periodic positive solution which asymptotically attracts every
other positive solution.
