This case study examines postgraduate students' practices, sources of knowledge, and difficulties and challenges in regard to providing genre-based peer feedback on their peers' academic writing at a research-oriented university in Macau. The analysis of multiple sources of data including the students' written feedback on their peers' thesis drafts, the thesis drafts, semi-structured interviews and stimulated recalls revealed that while the participants were able to provide genre-based feedback, most of the feedback focused on the linguistic features, content and organisation of the theses, and helped the students meet the institutional requirements of what constitutes a thesis. The study also found that the participants perceived giving genre-based peer feedback to be difficult and challenging. Their difficulties stemmed from a lack of specific knowledge about the thesis genre, their concerns about their own linguistic proficiency, their concerns about the usefulness and correctness of their feedback, and the effects their criticism would have on the writers' feelings and emotions.