Questions under Discussion (QUDs) have been suggested to influence the integration of individual utterances into a discourse-level representation. Previous work has shown that processing ungrammatical ellipses is facilitated when the elided material addresses an implicit QUD raised through a nonactuality implicature (NAIs). It is not clear, however, if QUDs influence discourse coherence during comprehension of fully acceptable discourse. We present two ERP studies examining the effects of QUDs introduced by NAIs using two-sentence discourses. Experiment 1 showed that processing definite NPs with inaccessible antecedents is facilitated when their content is relevant to the QUD. Using acceptable discourses, Experiment 2 showed that definite NPs failing to address a QUD elicit increased processing cost. Overall, our results indicate that QUDs raise the expectation that the following discourse will address them, providing unambiguous evidence that their influence is not limited to the processing of ungrammatical input.