Presuppositions convey information that comprehenders assume to be true, even when it is tangential to the communicator’s main message. For example, a class of verbs called ‘factives’ (e.g. realize, know) trigger the presupposition that the events or states conveyed by their sentential complements are true. In contrast, non-factive verbs (e.g. think, believe) do not trigger this presupposition. We asked whether, during language comprehension, presuppositions triggered by factive verbs are encoded within the comprehender’s discourse model, with neural consequences if violated by later bottom-up inputs. Using event-related potentials (ERPs), we examined neural activity to words that were either consistent or inconsistent with events/states conveyed by the complements of factive versus non-factive verbs while comprehenders read and actively monitored the coherence of short discourse scenarios. We focused on the modulation of a posteriorly-distributed late positivity or P600. This ERP component is produced when comprehenders constrain their discourse model such that it restricts predictions only to event structures that are compatible with this model, and new input violates these event structure predictions. Between 500-700ms, we observed a larger amplitude late posterior positivity/P600 on words that were inconsistent (versus consistent) with the events/states conveyed by the complements of factive verbs. No such effect was observed following non-factive verbs. These findings suggest that, during active discourse comprehension, the presuppositions triggered by factive verbs are encoded and maintained within the comprehender’s discourse model. Downstream input that is inconsistent with these presuppositions violates event structure predictions and conflicts with this prior model, producing the late posterior positivity/P600.