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 higher-order n-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 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.
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