We present in this paper a constraint-based account of robust parsing. More precisely, we propose a parsing technique relying on constraint satisfaction and its implementation by means of graphs. We show how constraint graphs constitute a flexible parsing framework both in terms of representation and implementation. They allow in particular to take into account non-connected elements, frequent in particular when parsing spoken languages. This approach is illustrated with some problematic examples (hesitations, phatics, repairs, etc.) taken from spoken french corpora.