This paper presents the formal definition and visual presentation of Dialogue graphs -- a visual specification technique for dialogue modelling. The Dialogue graphs are used in TADEUS to support an explicit dialogue modelling stage in a task-oriented and model-based approach to the development of interactive systems and automatic generation of the user interface code. The requirements of such a specification technique are discussed from different points of view. The formal definition of the Dialogue graphs is based on Coloured Petri net theory. The interactive tool for handling the Dialogue graphs is described shortly. The use of Dialogue graphs is demonstrated describing the OpenLook e-mail tool.