Discourse connectives are important indicators of textual coherence, and mastering them is an essential part of acquiring a language. In this article, we compare advanced learners' sensitivity to the meaning conveyed by connectives in an off-line grammaticality judgment task and an on-line reading experiment using eye-tracking. We also assess the influence of first language (L1) transfer by comparing learners' comprehension of two non-native-like semantic uses of connectives in English, often produced by learners due to transfer from French and Dutch. Our results indicate that in an off-line task transfer is an important factor accounting for French- and Dutch-speaking learners' non-native-like comprehension of connectives. During on-line processing, however, learners are as sensitive as native speakers to the meaning conveyed by connectives. These results raise intriguing questions regarding explicit vs. implicit knowledge in language learners.