‘Negative scope’ concerns what it is that is negated in an utterance with a negative morpheme. With English and Japanese conversational data, we show that for an English speaker, calculating negative scope requires that recipients incrementally keep track of all the material in the clause thatfollowsthe negative morpheme, which comes early in the clause. In contrast, the negative morpheme comes late in the clause in Japanese; thus it would seem that recipients need to hold in memory all the material in the clauseprecedingthe negative until the negative morpheme is produced. Several features of Japanese grammar, however, suggest that this characterization is not accurate. We argue that prosody, grammar, cognition, processing, and fixedness all interact with the grammar of clause organization to afford quite different real-time processing strategies for calculating the assignment of negative scope in languages with different ‘word order’ norms.