Using ERPs, we tested whether L2 speakers can integrate multiple sources of information (e.g., semantic, pragmatic information) during discourse comprehension. We presented native speakers and L2 speakers with three-sentence scenarios in which the final sentence was highly causally related, intermediately related, or causally unrelated to its context; its interpretation therefore required simple or complex inferences. Native speakers revealed a gradual N400-like effect, larger in the causally unrelated condition than in the highly related condition, and falling in-between in the intermediately related condition, replicating previous results. In the crucial intermediately related condition, L2 speakers behaved like native speakers, however, showing extra processing in a later time-window. Overall, the results show that, when reading, L2 speakers are able to process information from the local context and prior information (e.g., world knowledge) to build global coherence, suggesting that they process different sources of information to make inferences online during discourse comprehension, like native speakers.