This paper discusses the dynamic of context through the use of a context-based formalism called contextual graphs that has been initially developed in the SART application for the development of a support system in incident solving on a subway line. First, we present the formalism of contextual graphs through its new implementation. Second, we discuss the dynamic of context in contextual graphs. Third, we present two characteristics of contextual graphs as they relate to the dynamic of context, the incremental knowledge acquisition and the explanation generation. We conclude by a discussion of the key properties and the potential of contextual graphs for other applications.