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Narrative time has an important role to play in Interactive Storytelling (IS). The prevailing approach to controlling narrative time has been to use implicit models that allow only limited temporal reasoning about virtual agent behaviour. In contrast, this paper proposes the use of an explicit model of narrative time which provides a control mechanism that enhances narrative generation, orchestration of virtual agents and number of possibilities for the staging of agent actions. This approach can help address a number of problems experienced in IS systems both at the level of execution staging and at the level of narrative generation. Consequently it has a number of advantages: it is more flexible with respect to the staging of virtual agent actions; it reduces the possibility of timing problems in the coordination of virtual agents; and it enables more expressive representation of narrative worlds and narrative generative power. Overall it provides a uniform, consistent, principled and rigorous approach to the problem of time in agent-based storytelling. In the paper we demonstrate how this approach to controlling narrative time can be implemented within an IS system and illustrate this using our fully implemented IS system that features virtual agents inspired by Shakespeare's The Merchant of Venice. The paper presents results of an experimental evaluation with the system that demonstrates the use of this approach to co-ordinate the actions of virtual agents and to increase narrative generative power.