A distributed virtual environment (DVE) allows geographically separated users to participate in a shared virtual environment via connected networks. However, when the users are connected by the Internet, bandwidth limitation and network latency may seriously affect the performance and the interactivity of the system. This explains why there are very few DVE applications for the Internet. To address these shortcomings, caching and prefetching techniques are usually employed. Unfortunately, the effectiveness of these techniques depends largely on the accuracy of the prediction method used. Although there are a few methods proposed for predicting 3D motion, most of them are primarily designed for predicting the motion of specific objects by assuming certain object motion behaviors. We notice that in desktop DVE applications, such as virtual walkthrough and network gaming, the 2D mouse is still the most popular device used for navigation input. Through studying the motion behavior of a mouse during 3D navigation, we have developed a hybrid motion model for predicting the mouse motion during such navigation-a linear model for prediction at low-velocity motion and an elliptic model for prediction at high-velocity motion. The predicted mouse motion velocity is then mapped to the 3D environment for predicting the user's 3D motion. We describe how this prediction method can be integrated into the caching and prefetching mechanisms of our DVE prototype. We also demonstrate the effectiveness of the method and the resulting caching and prefetching mechanisms through extensive experiments.