Aims: Statins are pivotal to the secondary prevention of major adverse cardiovascular events, but some patients are statin-intolerant. We examined the effects of the proprotein convertase subtilisin/kexin type 9 (PCSK9) inhibitor alirocumab on the risk of major adverse cardiovascular events according to the intensity of background statin treatment. ----- Methods and results: The ODYSSEY OUTCOMES trial compared alirocumab with placebo in 18,924 patients with acute coronary syndrome and dyslipidaemia despite intensive or maximum-tolerated statin treatment (including no statin if intolerance was documented). The primary outcome (major adverse cardiovascular events) comprised coronary heart disease death, non-fatal myocardial infarction, ischaemic stroke, or unstable angina. Median follow-up was 2.8 years. Baseline statin treatment was high-intensity (88.8%), low/moderate-intensity (8.7%) or none (2.4%). Median baseline low-density lipoprotein cholesterol was 86, 89 and 139 mg/dL (P < 0.001) in these statin treatment categories, respectively. Alirocumab produced similar relative reductions in low-density lipoprotein cholesterol from baseline across statin treatment subgroups, but the mean absolute reductions differed (52.9, 56.7 and 86.1 mg/dL, respectively; P < 0.001). With placebo, the incidence of major adverse cardiovascular events was highest in the no statin subgroup (10.8%, 10.7% and 26.0% respectively). Alirocumab reduced major adverse cardiovascular events in each statin subgroup (hazard ratio 0.88, 95% confidence interval (CI) 0.80-0.96; 0.68, 0.49-0.94; and 0.65, 0.44-0.97, respectively; Pinteraction = 0.14) with a gradient of absolute risk reduction: 1.25%, 95% CI 0.34-2.16; 3.16%, 0.38-5.94; 7.97%, 0.42-15.51; Pinteraction = 0.106). ----- Conclusions: PCSK9 inhibition with alirocumab reduces the relative risk of major adverse cardiovascular events after acute coronary syndrome irrespective of background statin treatment. However, patients on no statin are at high absolute risk for recurrent major adverse cardiovascular events; alirocumab substantially reduces that risk. PCSK9 inhibition may be an important therapeutic strategy for statin-intolerant patients with acute coronary syndrome.