Spatial concentrations (or spatial clusters) of moving objects, such as vehicles and humans, is a mobility pattern that is relevant to many applications. A fast detection of this pattern and its evolution, e.g., if the cluster is shrinking or growing, is useful in numerous scenarios, such as detecting the formation of traffic jams or detecting a fast dispersion of people in a music concert. An on-line detection of this pattern is a challenging task because it requires algorithms that are capable of continuously and efficiently processing the high volume of position updates in a timely manner. Currently, the majority of approaches for spatial cluster detection operate in batch mode, where moving objects location updates are recorded during time periods of certain length and then batch-processed by an external routine, thus delaying the result of the cluster detection until the end of the time period. Further, they extensively use spatial data structures and operators, which can be troublesome to maintain or parallelize in on-line scenarios. To address these issues, in this thesis we propose DG2CEP, an algorithm that combines the well-known density-based clustering algorithm DBSCAN with the data stream processing paradigm Complex Event Processing (CEP) to achieve continuous and timely detection of spatial clusters. Our experiments with real world data streams indicate that DG2CEP is able to detect the formation and dispersion of clusters with small latency while having a higher similarity to DBSCAN than batch-based approaches.