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E-business software systems are typically incorporated in complex concurrent and interacting business activities. Understanding the concurrent and interactive demands of the environment and tracing these requirements down to implementation is an important and necessary part of developing these types of systems. In this paper, we illustrate how concurrency concerns can be integrated in a UML-based software development method, and how these concerns can be incrementally refined from requirements to implementations. Our proposed approach not only offers a much needed holistic approach to concurrency in software development, but it also offers some novel techniques to describe concurrency concerns at each level of UML description.