  Hybrid logic with binders is an expressive specification language. Its
satisfiability problem is undecidable in general. If frames are restricted to N
or general linear orders, then satisfiability is known to be decidable, but of
non-elementary complexity. In this paper, we consider monotone hybrid logics
(i.e., the Boolean connectives are conjunction and disjunction only) over N and
general linear orders. We show that the satisfiability problem remains
non-elementary over linear orders, but its complexity drops to
PSPACE-completeness over N. We categorize the strict fragments arising from
different combinations of modal and hybrid operators into NP-complete and
tractable (i.e. complete for NC1or LOGSPACE). Interestingly, NP-completeness
depends only on the fragment and not on the frame. For the cases above NP,
satisfiability over linear orders is harder than over N, while below NP it is
at most as hard. In addition we examine model-theoretic properties of the
fragments in question.
