Understanding alternatives to prominent information contributes to successful native language discourse comprehension. Several past studies have suggested that the way second language (L2) learners encode and represent an alternative set in L2 speech is not exactly native-like. However, because these studies involved contrastive pitch accents in running speech, these native language–second language differences may reflect the demands of comprehending running speech in L2 rather than intrinsic deficit in discourse processing per se. Here, we tested L2 learners’ discourse encoding and representation using a different cue to prominence: font emphasis in self-paced reading. We found that, in this temporally less demanding modality, L2 learners’ encoding of salient alternatives became native-like. Font emphasis facilitated L2 learners’ memory for the discourse by ruling out salient alternatives, just as how it facilitates native speakers’. L2 learners were also similar to native speakers in using the situation model to constrain an alternative set. The results suggest that L2 learners can show native-like processing of prominence and that previous underuse of contrastive accents in L2 comprehension could reflect cognitive demands of processing running speech in L2.