In this work we consider the problem of continuously monitoring a collection of data sets produced by sensors placed on moving or static targets. We propose a modification of the static sensor field model (SSSF) [2] to model computation in a dynamic network of tiny artifacts. We consider mobility coming from both the communication devices and the data. The mobility of devices is simulated by a dynamic communication graph. Data mobility is due to measurements performed by sensing devices that are not placed on fixed positions but attached to mobile agents. Accordingly, we introduce additional performance measures: the traveled distance and the gathering period. We study the Continuous Monitoring problem providing bounds on performance for algorithms that use mobility in different ways.