The present study uses self-paced reading as a measure of online processing and an acceptability judgement task as a measure of offline explicit linguistic knowledge, to understand L2 learners’ comprehension processes and their awareness of subtle differences between the modal auxiliaries may and can. Participants were two groups of university students: 42 native speakers of English and 41 native speakers of Croatian majoring in L2 English. The study is part of a larger project which has provided empirical evidence of the two modals, may and can, being mutually exclusive when denoting ability (can) and epistemic possibility (may), but equally acceptable in pragmatic choices expressing permission. The present results revealed that L1 and L2 speakers rated the acceptability of sentences in offline tasks similarly; however, L2 learners showed no sensitivity to verb context mismatches in epistemic modality, while demonstrating sensitivity when processing modals expressing ability. Implications for L2 acquisition of modals and future research are discussed.