Background Ticagrelor is an effective antiplatelet therapy for patients with coronary atherosclerotic disease and might be more effective than aspirin in preventing recurrent stroke and cardiovascular events in patients with acute cerebral ischaemia of atherosclerotic origin. Our aim was to test for a treatment-by-ipsilateral atherosclerotic stenosis interaction in a subgroup analysis of patients in the Acute Stroke or Transient Ischaemic Attack Treated with Aspirin or Ticagrelor and Patient Outcomes (SOCRATES) trial. Methods SOCRATES was a randomised, double-blind, controlled trial of ticagrelor versus aspirin in patients aged 40 years or older with a non-cardioembolic, non-severe acute ischaemic stroke, or high-risk transient ischaemic attack from 674 hospitals in 33 countries. We randomly allocated patients (1: 1) to ticagrelor (180 mg loading dose on day 1 followed by 90 mg twice daily for days 2-90, given orally) or aspirin (300 mg on day 1 followed by 100 mg daily for days 2-90, given orally) within 24 h of symptom onset. Investigators classified all patients into atherosclerotic and non-atherosclerotic groups for the prespecified, exploratory analysis reported in this study. The primary endpoint was the time to occurrence of stroke, myocardial infarction, or death within 90 days. Efficacy analysis was by intention to treat. The SOCRATES trial is registered with ClinicalTrials.gov, number NCT01994720. Findings Between Jan 7, 2014, and Oct 29, 2015, we randomly allocated 13 199 patients (6589 [50%] to ticagrelor and 6610 [50%] to aspirin). Potentially symptomatic ipsilateral atherosclerotic stenosis was reported in 3081 (23%) of 13 199 patients. We found a treatment-by-atherosclerotic stenosis interaction (p=0.017). 103 (6.7%) of 1542 patients with ipsilateral stenosis in the ticagrelor group and 147 (9.6%) of 1539 patients with ipsilateral stenosis in the aspirin group had an occurrence of stroke, myocardial infarction, or death within 90 days (hazard ratio 0.68 [95% CI 0.53-0.88]; p=0.003). In 10 118 patients with no ipsilateral stenosis, 339 (6.7%) of 5047 patients in the ticagrelor group had an occurrence of stroke, myocardial infarction, or death within 90 days compared with 350 (6.9%) of 5071 in the aspirin group (0.97 [0.84-1.13]; p=0.72). There were no significant differences in the proportion of life-threatening bleeding or major or minor bleeding events in patients with ipsilateral stenosis in the ticagrelor group compared with the aspirin group. Interpretation In this prespecified exploratory analysis, ticagrelor was superior to aspirin at preventing stroke, myocardial infarction, or death at 90 days in patients with acute ischaemic stroke or transient ischaemic attack when associated with ipsilateral atherosclerotic stenosis. An understanding of stroke mechanisms and causes is important to deliver safe and efficacious treatments for early stroke prevention.