Identifying undiagnosed obstructive sleep apnoea (OSA) patients in cardiovascular clinics could improve their management. Aiming to build an OSA predictive model, a broad analysis of clinical variables was performed in a cohort of acute coronary syndrome (ACS) patients. Sociodemographic, anthropometric, life-style and pharmacological variables were recorded. Clinical measures included blood pressure, electrocardiography, echocardiography, blood count, troponin levels and a metabolic panel. OSA was diagnosed using respiratory polygraphy. Logistic regression models and classification and regression trees were used to create predictive models. A total of 978 patients were included (298 subjects with apnoea–hypopnoea index (AHI) <15 events•h −1 and 680 with AHI ≥15 events•h −1). Age, BMI, Epworth sleepiness scale, peak troponin levels and use of calcium antagonists were the main determinants of AHI ≥15 events•h −1 (C statistic 0.71; sensitivity 94%; specificity 24%). Age, BMI, blood triglycerides, peak troponin levels and Killip class ≥II were determinants of AHI ≥30 events•h −1 (C statistic of 0.67; sensitivity 31%; specificity 86%). Although a set of variables associated with OSA was identified, no model could successfully predict OSA in patients admitted for ACS. Given the high prevalence of OSA, the authors propose respiratory polygraphy as a to-be-explored strategy to identify OSA in ACS patients.