  The exponential ordering is exploited in the context of non-auto\-no\-mous
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.
