Academic reading in English requires processing of challenging advanced texts for comprehension. highly proficient second language (L2) readers, such as graduate students, are expected to interpret complex texts fluently and efficiently for academic success, yet the field has little evidence on how these readers process texts. Through two think-aloud reading sessions and pre- and postreading interviews, this study closely examined nine graduate students' interactions with texts that had low and high levels of discourse cohesion. The focus was on the readers' meaning-construction process in relation to the texts' cohesion. The researchers analyzed these data qualitatively using a grounded theory approach that revealed text-processing activities of proficient L2 readers grouped at local and global levels. Although all readers experienced these two levels with both texts, some differences were found in their processing between two texts, especially in reading the low-cohesive text. The findings of the study provide implications for reading instructors and teacher researchers in understanding how advanced L2 readers construct meaning and draw on text discourse as they read texts in English and potentially in conceptualizing what novice L2 readers must do to progress.