While distributed systems with transfer of processes have become
pervasive, methods for reasoning about their behaviour are
underdeveloped. In this paper we propose a bisimulation technique for
proving behavioural equivalence of such systems modelled in the
\emph{higher-order $\pi$-calculus with passivation} (and restriction).
Previous research for this calculus is limited to context
bisimulations and normal bisimulations which are either impractical or
unsound. In contrast, we provide a sound and useful definition of
\emph{environmental bisimulations}, with several non-trivial examples.
Technically, a central point in our bisimulations is the clause for
parallel composition, which must account for passivation of the
spawned processes in the middle of their execution.