In this paper we study the evaluation of continuous constraint queries (CCQs) for spatiotemporal streams. A CCQ triggers an alert whenever a configuration of constraints between streaming events in space and time are satisfied. Consider, for instance, a server that receives updates from GPS-enabled agents that report their positions and other measurements (e.g., environmental readings). An example of CCQ is: “Alert whenever at least 5 readings closer than 5km to each other and within a time difference of 5 minutes report high pressures and low temperatures”. We model CCQs as Constraint Satisfaction Problems (CSPs) and develop solutions for their continuous evaluation. Our techniques (1) consider the fast arrival rate of incoming events, and (2) minimize the memory requirements, without using predefined window constraints, but by utilizing the structure of the queries. In order to show the merits of the proposed techniques, we implement a system prototype and evaluate it with rea...