An increasing amount of Web services are being implemented using process management tools and languages (BPML, BPEL, etc.). The main advantage of processes is that designers can express complex business conversations at a high level of abstraction, even reusing standardized business protocols. The downside is that the infrastructure behind the Web service becomes more complex. This is particularly critical for Web services that may be subjected to high variability in demand and suffer from unpredictable peaks of heavy load. In this paper we present a flexible architecture for process execution that has been designed to support autonomic scalability. The system runs on a cluster of computers and reacts to workload variations by altering its configuration in order to optimally use the available resources. Such changes happen automatically and without any human intervention. This feature completely removes the need for the manual monitoring and reconfiguration of the system, which in practice is a difficult and time-consuming operation. In the paper we describe the architecture of the system and present an extensive performance evaluation of its autonomic capabilities.