Availability of precise, yet usable modeling languages is essential to the construction of multimedia systems based on software engineering principles and methods. Although several languages have been proposed for the specification of isolated multimedia system aspects, there not yet exists an integrated modeling language that adequately supports multimedia software development in practice. We propose an extension of the Unified Modeling Language (UML) for the integrated specification of multimedia systems based on an object-oriented development method. Since integration of co-existing timed procedural and interactive behavior is at the heart of multimedia systems, we focus on UML-based specification of behavior in this paper. In addition, we outline how these behavioral aspects are to be integrated with media, presentation, and software architecture modeling to achieve a coherent and consistent model.