The concept of synchronous programming has been proposed and widely accepted in the design of real-time systems, circuits, and embedded systems. Some recent researches have also proposed a mechanism to distribute a synchronous system over asynchronous networks. Meanwhile, UML is also becoming a standard framework of object-oriented methodologies. Our research aims to take advantage of these rich backgrounds by integrating a synchronous pivot called SPOTS (synchronous pre-order transition system) into UML and to propose a new methodology for the development of real-time distributed systems. In this paper, we focus on the issue of UML state-machines. We first present a recursive structure of UML state-machines. Compared with earlier studies, this structure supports composite transitions and histories. After a brief introduction to the pivot SPOTS, we will concentrate on the formal semantics of We will also give some complete examples of the translation according to the prototype we have implemented.