In this paper we investigate how consistency can be ensured for replicated continuous interactive media, i.e., replicated media which change their state in reaction to user initiated operations as well as because of the passing of time. Typical examples for this media class are networked computer games and distributed VR applications. Existing approaches to reach consistency for replicated discrete interactive media are briefly outlined and it is shown that these fail in the continuous domain. In order to allow a thorough discussion of the problem, a formal definition of the term consistency in the continuous domain is given. Based on this definition we show that an important tradeoff relationship exists between the responsiveness of the medium and the appearance of short-term inconsistencies. Until now this tradeoff was not taken into consideration for consistency in the continuous domain, thereby severely limiting the consistency related fidelity for a large number of applications. ...