The use of Shared Virtual Environments is growing in areas such as multi-player video games, military and industrial training, and collaborative design and engineering. At the same rate, different mixes of computing power and graphics capabilities of the participating computers arises naturally as the variety of people/organizations sharing a virtual environment grows. This paper presents an adaptive mechanism to reduce bandwidth usage and to optimize the use of computing resources of heterogeneous computers mixes participating in a shared virtual environment. It is based on caching of both outgoing- and incoming-messages. We also report the results of implementing the proposed scheme in a simple shared virtual environment. Keywords Virtual Reality, Shared Virtual Environments, Message Caching, Networking.