In Virtual Reality applications, polygons are widely used in object rep resentation because of its mathematical simplicity and support by existing hardware graphics accelerators. However, there are numerous objects inside a Distributed Virtual Environment (DVE), and large number of polygons are required to represent a detailed and complex DVE. Rendering time increases with the number of polygons and long rendering latency is resulted. Besides, a complex DVE also takes longer time to transmit over network. The rendering and transmission latency slowed down the display frame rate, and user's sense of presence inside the DVE is affected. Multi-resolution Modeling (MrM) approach reduces the rendering latency of a complex DVE by substituting visually less perceivable objects (e.g. distant objects) with lower resolution models. Hence, the total polygon number in the scene is reduced with little visual degradation. Besides, usually only part of a large sized object, such as a terrain, is visible to the user at a time. We can further reduce the polygon number by Adaptive hIrhI methods where only regions within the user's view frustum is refined. On the other hand, transmission of multi-resolution models has not been considered until recently. Progressive transmission alleviates the problem of transmission latency by first transmitting a low resolution model to the client to provide an instant visual feedback to the user. Refinement records are then transmitted in order and the model is refined progressively. This solution may also work on the Adaptive MrM methods as well. However, as the order of record transmission is predefined, the model cannot be adaptively transmitted. Invisible parts of the model may be transmitted before visible parts and the network bandwidth is not well utilized. This problem becomes significant for DVE over slow speed network, like the Internet, where bandwidth is limited and connection is occasionally lost. This dissertation presents a real-time MrM approach for maintaining constant frame rate and optimizing transmission performance in DVE over slow speed network. Two transmission optimized Mrh methods have been proposed, namely Non-adaptive MrM method and Adaptive MrM method. The Non-adaptive MrM method with progressive transmission is proposed for small sized objects. It has been used in a DVE system over the Internet, and its performance is found to be improved when using with multi-resolution caching and pre-fetching mechanisms. The Adaptive MrM method with selective and progressive transmission is proposed for large sized objects. Visually important parts of the object can be transmitted at a higher priority than the less important parts. Only visible part of the model is stored at the client and memory storage is saved. Moreover, the adaptive model is constructed from the partially transmitted model without the need of recursive dependency checkings, which are needed in existing methods.