  This paper is devoted to the study of nonautonomous multivalued semiflows and
their associated pullback attractors. For this kind of dynamical systems we are
able to characterize the upper and lower bounds of the attractor as complete
trajectories belonging to the attractor, so that all the internal dynamics is
confined in this region, which can be described as an interval due to the
orderly nature of the processes. Thus, we are able to generalize to this
framework previous general results in literature for autonomous multivalued
flows or nonautonomous differential equations. We apply our results to a
partial differential inclusion with a nonautonomous term, also proving the
upper semicontinuity dependence of pullback and global attractors when the time
dependent term asymptotically converges to an autonomous multivalued term.
