This paper proposes a method for incrementally understanding user utterances whose semantic boundaries are not known and responding in real time even before boundaries are determined. It is an integrated parsing and discourse processing method that updates the partial result of understanding word by word, enabling responses based on the partial result. This method incrementally finds plausible sequences of utterances that play crucial roles in the task execution of dialogues, and utilizes beam search to deal with the ambiguity of boundaries as well as syntactic and semantic ambiguities. .