  Hyperproperties have received increasing attention in the last decade due to
their importance e.g. for security analyses. Past approaches have focussed on
synchronous analyses, i.e. techniques in which different paths are compared
lockstepwise. In this paper, we systematically study asynchronous analyses for
hyperproperties by introducing both a novel automata model (Alternating
Asynchronous Parity Automata) and the temporal fixpoint calculus $\Hmu$, the
first fixpoint calculus that can systematically express hyperproperties in an
asynchronous manner and at the same time subsumes the existing logic HyperLTL.
We show that the expressive power of both models coincides over fixed path
assignments. The high expressive power of both models is evidenced by the fact
that decision problems of interest are highly undecidable, i.e. not even
arithmetical. As a remedy, we propose approximative analyses for both models
that also induce natural decidable fragments.
