Distributed Interactive Applications (DIAs) have been gaining commercial success in recent years due to the widespread appeal of networked multiplayer computer games. Within these games, participants interact with each other and their environment, producing complex behavioural patterns that evolve over time. These patterns are nonlinear, and often appear to exhibit dependencies under certain conditions. In this paper, we analyse the behavioural patterns of two participants interacting in a DIA. Our motivation behind this analysis is to construct models of user behaviour that can be used for prediction within Entity-State-Update (ESU) mechanisms. By representing their behaviour as time-series datasets, we investigate the use of simple statistical dependence measures to help partition the datasets and identify three different types of behavioural states exhibited by the two participants. It is our intention that future research on ESU mechanisms can utilize this behavioural partitioning to reduce the network traffic in a DIA based on a hybrid-model approach.