This paper tackles the problem of designing and programming a real-time system with multiple modes of execution, where each mode executes a different set of periodic tasks. The main problem to tackle is that the period of Mode Change Requests (MCR) and the period of tasks are not all the same. Thus, not all tasks perceive MCRs in the same way. When programming such a system with traditional languages without mechanisms dedicated to mode changes (e.g. C), it is difficult to ensure a system is sound and deterministic. We propose an extension to synchronous dataflow languages to support mode changes. The semantics of the resulting language is defined formally, which prevents ambiguous programs. The language is flexible enough to support different types of mode changes. The compiler of the language includes a static analysis that rejects programs whose semantics is ill-defined. The extension consists in transposing Synchronous State Machines to the PRELUDE language. This requires to extend the semantics of PRELUDE, and to define a new clock calculus, based on refinement typing.