New sensor technologies, powerful mobile devices, and wireless communication standards strongly proliferate ubiquitous and pervasive computing. This is particularly true for healthcare applications. Modern non-invasive unobtrusive sensors enable sophisticated monitoring of the human body. As a result of this monitoring a growing amount of elderly people suffering from chronic diseases will benefit from an enhanced quality of life and improved treatment. Healthcare applications process a vast amount of continuously generated data, this has become a serious challenge. Data stream management addresses this problem in general. However, healthcare applications have additional requirements, e.g., flexibility and reliability. As a consequence, we propose the combination of a sophisticated information infrastructure, called hyperdatabase, and data stream management. Hyperdatabases already allow for reliable process management in a peer-to-peer fashion. In this paper, we elaborate the close relation between distributed process management and data stream management. Further, we show that data stream processing can significantly benefit from an infrastructure for reliable process management. We present the architecture of our prototype infrastructure that supports processing of continuous data streams with a high degree of flexibility and reliability.