Background Long-term postoperative cognitive dysfunction may occur in the elderly. Age may be a risk factor and hypoxaemia and arterial hypotension causative factors. We investigated these hypotheses in an international multicentre study. Methods 1218 patients aged at least 60 years completed neuropsychological tests before and 1 week and 3 months after major non-cardiac surgery. We measured oxygen saturation by continuous pulse oximetry before surgery and throughout the day of and the first 3 nights after surgery. We recorded blood pressure every 3 min by oscillometry during the operation and every 15–30 min for the rest of that day and night. We identified postoperative cognitive dysfunction with neuropsychological tests compared with controls recruited from the UK (n=176) and the same countries as study centres (n=145). Findings Postoperative cognitive dysfunction was present in 266 (25·8% [95% CI 23·1–28·5]) of patients 1 week after surgery and in 94 (9·9% [8·1–12·0]) 3 months after surgery, compared with 3·4% and 2·8%, respectively, of UK controls (p<0·0001 and p=0·0037, respectively). Increasing age and duration of anaesthesia, little education, a second operation, postoperative infections, and respiratory complications were risk factors for early postoperative cognitive dysfunction, but only age was a risk factor for late postoperative cognitive dysfunction. Hypoxaemia and hypotension were not significant risk factors at any time. Interpretation Our findings have implications for studies of the causes of cognitive decline and, in clinical practice, for the information given to patients before surgery.