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Postoperative respiratory failure (PRF) is the most frequent respiratory complication following surgery.The objective of this study was to build a clinically useful predictive model for the development of PRF.A prospective observational study of a multicentre cohort.Sixty-three hospitals across Europe.Patients undergoing any surgical procedure under general or regional anaesthesia during 7-day recruitment periods.Development of PRF within 5 days of surgery. PRF was defined by a partial pressure of oxygen in arterial blood (PaO2) less than 8 kPa or new onset oxyhaemoglobin saturation measured by pulse oximetry (SpO2) less than 90% whilst breathing room air that required conventional oxygen therapy, noninvasive or invasive mechanical ventilation.PRF developed in 224 patients (4.2% of the 5384 patients studied). In-hospital mortality [95% confidence interval (95% CI)] was higher in patients who developed PRF [10.3% (6.3 to 14.3) vs. 0.4% (0.2 to 0.6)]. Regression modelling identified a predictive PRF score that includes seven independent risk factors: low preoperative SpO2; at least one preoperative respiratory symptom; preoperative chronic liver disease; history of congestive heart failure; open intrathoracic or upper abdominal surgery; surgical procedure lasting at least 2 h; and emergency surgery. The area under the receiver operating characteristic curve (c-statistic) was 0.82 (95% CI 0.79 to 0.85) and the Hosmer–Lemeshow goodness-of-fit statistic was 7.08 (P = 0.253).A risk score based on seven objective, easily assessed factors was able to predict which patients would develop PRF. The score could potentially facilitate preoperative risk assessment and management and provide a basis for testing interventions to improve outcomes.The study was registered at ClinicalTrials.gov (identifier NCT01346709).