Background: An association between increasing anaesthetic depth and decreased postoperative survival has been shown in observational studies; however, evidence from randomised controlled trials is lacking. Our aim was to compare all-cause 1-year mortality in older patients having major surgery and randomly assigned to light or deep general anaesthesia. Methods: In an international trial, we recruited patients from 73 centres in seven countries who were aged 60 years and older, with significant comorbidity, having surgery with expected duration of more than 2 h, and an anticipated hospital stay of at least 2 days. We randomly assigned patients who had increased risk of complications after major surgery to receive light general anaesthesia (bispectral index [BIS] target 50) or deep general anaesthesia (BIS target 35). Anaesthetists also nominated an appropriate range for mean arterial pressure for each patient during surgery. Patients were randomly assigned in permuted blocks by region immediately before surgery, with the patient and assessors masked to group allocation. The primary outcome was 1-year all-cause mortality. The trial is registered with the Australian New Zealand Clinical Trials Registry, ACTRN12612000632897, and is closed to accrual. Findings: Patients were enrolled between Dec 19, 2012, and Dec 12, 2017. Of the 18 026 patients screened as eligible, 6644 were enrolled, randomly assigned to treatment or control, and formed the intention-to-treat population (3316 in the BIS 50 group and 3328 in the BIS 35 group). The median BIS was 47·2 (IQR 43·7 to 50·5) in the BIS 50 group and 38·8 (36·3 to 42·4) in the BIS 35 group. Mean arterial pressure was 3·5 mm Hg (4%) higher (median 84·5 [IQR 78·0 to 91·3] and 81·0 [75·4 to 87·6], respectively) and volatile anaesthetic use was 0·26 minimum alveolar concentration (30%) lower (0·62 [0·52 to 0·73] and 0·88 [0·74 to 1·04], respectively) in the BIS 50 than the BIS 35 group. 1-year mortality was 6·5% (212 patients) in the BIS 50 group and 7·2% (238 patients) in the BIS 35 group (hazard ratio 0·88, 95% CI 0·73 to 1·07, absolute risk reduction 0·8%, 95% CI −0·5 to 2·0). Grade 3 adverse events occurred in 954 (29%) patients in the BIS 50 group and 909 (27%) patients in the BIS 35 group; and grade 4 adverse events in 265 (8%) and 259 (8%) patients, respectively. The most commonly reported adverse events were infections, vascular disorders, cardiac disorders, and neoplasms. Interpretation: Among patients at increased risk of complications after major surgery, light general anaesthesia was not associated with lower 1-year mortality than deep general anaesthesia. Our trial defines a broad range of anaesthetic depth over which anaesthesia may be safely delivered when titrating volatile anaesthetic concentrations using a processed electroencephalographic monitor. Funding: Health Research Council of New Zealand; National Health and Medical Research Council, Australia; Research Grant Council of Hong Kong; National Institute for Health and Research, UK; and National Institutes of Health, USA.