  We study the satisfiability and model-checking problems for timed
hyperproperties specified with HyperMTL, a timed extension of HyperLTL.
Depending on whether interleaving of events in different traces is allowed, two
possible semantics can be defined for timed hyperproperties: asynchronous and
synchronous. While the satisfiability problem can be decided similarly to
HyperLTL regardless of the choice of semantics, we show that the model-checking
problem, unless the specification is alternation-free, is undecidable even when
very restricted timing constraints are allowed. On the positive side, we show
that model checking HyperMTL with quantifier alternations is possible under
certain conditions in the synchronous semantics, or when there is a fixed bound
on the length of the time domain.
