Millstream systems have been proposed as a non-hierarchical method for modelling natural language. Millstream configurations represent and connect multiple structural aspects of sentences. We present a method by which the Millstream configurations corresponding to a sentence are constructed. The construction is incremental, that is, it proceeds as the sentence is being read and is complete when the end of the sentence is reached. It is based on graph transformations and a lexicon which associates words with rules for the graph transformations.