Bilingual students with a migrant background are often misplaced in specialized education programs intended for students with learning disabilities because of their weaknesses in academic language ability (Hulse & Curran, 2020). The aim of this qualitative research was to explore the views of secondary education teachers in Greece regarding the academic characteristics of their bilingual students with a migrant background in relation to those of dyslexic students. The data collection and analysis took place in 2022. The participants were 71 teachers who answered an open-ended questionnaire, among whom five teachers additionally participated in in-depth qualitative interviews. The study showed that the secondary school teachers were not aware of the bilingual reality in their classrooms and that they hardly recognized their own inadequacy in appropriately distinguishing between bilingual and dyslexic students. Therefore, they seemed to avoid assuming responsibility for ineffectively dealing with the issue and not addressing students’ needs. The study demonstrates the imperative need to make appropriate decisions at the level of teachers’ education and training to adequately support both bilingual students with a migrant background and dyslexic students.