Processing of continuous data streams is emerging as an expanding area of research and concerns the processing of information from sources that produce data in a fast rate and in a continuous way. For example, information from sensory devices can be considered as a continuously expanding and unlimited sequence of data items without any boundaries. Traditionally, such information required special monitoring applications and equipment that process and react to continual inputs from several sources such as in a weather monitoring station, patient monitoring equipment, etc. This thesis concerns the processing of fast evolving data streams in relational database management systems. It investigates the utilization of existing features in a DBMS and their adoption to process infinite data streams and discusses the performance of the proposed solution. It provides a solution to the inherent limitations in the architecture of a DBMS to be able to react to continual inputs from several sources. The outcome of this thesis shows that it is possible to process continuous data streams from several sources and in some ways a better performance was also achievable.