Background It is unclear whether radial compared with femoral access improves outcomes in unselected patients with acute coronary syndromes undergoing invasive management. Methods We did a randomised, multicentre, superiority trial comparing transradial against transfemoral access in patients with acute coronary syndrome with or without ST-segment elevation myocardial infarction who were about to undergo coronary angiography and percutaneous coronary intervention. Patients were randomly allocated (1: 1) to radial or femoral access with a web-based system. The randomisation sequence was computer generated, blocked, and stratified by use of ticagrelor or prasugrel, type of acute coronary syndrome (ST-segment elevation myocardial infarction, troponin positive or negative, non-ST-segment elevation acute coronary syndrome), and anticipated use of immediate percutaneous coronary intervention. Outcome assessors were masked to treatment allocation. The 30-day coprimary outcomes were major adverse cardiovascular events, defined as death, myocardial infarction, or stroke, and net adverse clinical events, defined as major adverse cardiovascular events or Bleeding Academic Research Consortium (BARC) major bleeding unrelated to coronary artery bypass graft surgery. The analysis was by intention to treat. The two-sided a was prespecified at 0.025. The trial is registered at ClinicalTrials.gov, number NCT01433627. Findings We randomly assigned 8404 patients with acute coronary syndrome, with or without ST-segment elevation, to radial (4197) or femoral (4207) access for coronary angiography and percutaneous coronary intervention. 369 (8.8%) patients with radial access had major adverse cardiovascular events, compared with 429 (10.3%) patients with femoral access (rate ratio [RR] 0.85, 95% CI 0.74-0.99; p = 0.0307), non-significant at a of 0.025. 410 (9.8%) patients with radial access had net adverse clinical events compared with 486 (11.7%) patients with femoral access (0.83, 95% CI 0.73-0.96; p = 0.0092). The difference was driven by BARC major bleeding unrelated to coronary artery bypass graft surgery (1.6% vs 2.3%, RR 0.67, 95% CI 0.49-0.92; p= 0.013) and all-cause mortality (1.6% vs 2.2%, RR 0.72, 95% CI 0.53-0.99; p = 0.045). Interpretation In patients with acute coronary syndrome undergoing invasive management, radial as compared with femoral access reduces net adverse clinical events, through a reduction in major bleeding and all-cause mortality. Funding The Medicines Company and Terumo.