This paper investigates presheaf models for process calculi with<br />value passing. Denotational semantics in presheaf models are shown<br />to correspond to operational semantics in that bisimulation obtained<br />from open maps is proved to coincide with bisimulation as defined<br />traditionally from the operational semantics. Both "early" and "late"<br />semantics are considered, though the more interesting "late" semantics<br />is emphasised. A presheaf model and denotational semantics is proposed<br />for a language allowing process passing, though there remains<br />the problem of relating the notion of bisimulation obtained from open<br />maps to a more traditional definition from the operational semantics.<br />A tentative beginning is made of a "domain theory" supporting<br />presheaf models.