With sensors and mobile devices becoming ubiquitous, situation monitoring applications are becoming a reality. Data Stream Management Systems (DSMSs) have been proposed to address the data processing needs of such applications that require collection of high-speed data, computing results on-the-fly, and taking actions in real-time. Although a lot of work appears in the area of DSMS, not much has been done in multilevel secure (MLS) DSMS making the technology unsuitable for highly sensitive applications such as battlefield monitoring. An MLS DSMS should ensure the absence of illegal information flow in a DSMS and more importantly provide the performance needed to handle continuous queries. We investigate the issues important in an MLS DSMS and propose an architecture that best meets the goals of MLS DSMS. We discuss how continuous queries can be executed in such a system and sharing across queries accomplished for maximum performance benefits.