Cluster computing, whereby a large number of simple processors or nodes are combined together to apparently function as a single powerful computer, has emerged as a research area in its own right. The approach offers a relatively inexpensive means of achieving significant computational capabilities for high-performance computing applications, while simultaneously affording the ability to increase that capability simply by adding more (inexpensive) processors. However, the task of manually managing and configuring a cluster quickly becomes impossible as the cluster grows in size. Autonomic computing is a relatively new approach to managing complex systems that can potentially solve many of the problems inherent in cluster management. We describe the development of a prototype Automatic Cluster Management System (ACMS) that exploits autonomic properties in automating cluster management.