In this paper, a new approach for on-line handwritten structured document interpretation is presented. It aims at interpreting the strokes progressively. The major component of our approach is a flexible formalism for the recognition of the document elements. Its originality is the modelling of the document global structure. The system then drives dedicated recognizers and looks only for the likely symbols depending on the document structural context in which that element is located. Moreover, the formalism defines a "canonical on-line signal form" of the recognizer entries to facilitate the interpretation process which is then more robust and more efficient. To highlight its genericity, this approach has been used to design two pen-based prototypes, for musical score editing and for graph editing.