For native (L1) comprehenders, lower-level language processes such as lexical access and parsing are considered to consume few cognitive resources. In contrast, these processes pose considerable demands for second-language (L2) comprehenders. Two reading-time experiments employing inconsistency detection found that English learners did not detect an inconsistency unless contradicting parts were adjacent. This suggests that the text memory that L2 comprehenders can access online is an immediately preceding sentence. This makes a sharp contrast with the finding of previous research that L1 comprehenders appeared to retrieve an earlier portion that was several sentences away. A third experiment with probe verification suggested that L2 participants did not reactivate prior text information when reading the contradicting sentence following an intervening sentence. These results provide evidence for the limited resource allocation for discourse-level processes in L2 comprehension. The results are discussed based on the two-stage model that consists of the resonance and integration processes.