Data-intensive, interactive applications are an important class of metacomputing (Grid) applications. They are characterized by large, time-varying data flows between data providers and consumers. The topic of this paper is the runtime adaptation of data streams, in response to changes in resource availability and/or in end user requirements, with the goal of continually providing to consumers data at the levels of quality they require. Our approach is one that associates computational objects with data streams. Runtime adaptation is achieved by adjusting objects' actions on streams, by splitting and merging objects, and by migrating them (and the streams on which they operate) across machines and network links. Adaptive streams also react to changes in resource availability detected by online monitoring.