Background: Near-infrared spectroscopy (NIRS) and intravascular ultrasound are promising imaging modalities to identify non-obstructive plaques likely to cause coronary-related events. We aimed to assess whether combined NIRS and intravascular ultrasound can identify high-risk plaques and patients that are at risk for future major adverse cardiac events (MACEs). Methods: PROSPECT II is an investigator-sponsored, multicentre, prospective natural history study done at 14 university hospitals and two community hospitals in Denmark, Norway, and Sweden. We recruited patients of any age with recent (within past 4 weeks) myocardial infarction. After treatment of all flow-limiting coronary lesions, three-vessel imaging was done with a combined NIRS and intravascular ultrasound catheter. Untreated lesions (also known as non-culprit lesions) were identified by intravascular ultrasound and their lipid content was assessed by NIRS. The primary outcome was the covariate-adjusted rate of MACEs (the composite of cardiac death, myocardial infarction, unstable angina, or progressive angina) arising from untreated non-culprit lesions during follow-up. The relations between plaques with high lipid content, large plaque burden, and small lumen areas and patient-level and lesion-level events were determined. This trial is registered with ClinicalTrials.gov, NCT02171065. Findings: Between June 10, 2014, and Dec 20, 2017, 3629 non-culprit lesions were characterised in 898 patients (153 [17%] women, 745 [83%] men; median age 63 [IQR 55–70] years). Median follow-up was 3·7 (IQR 3·0–4·4) years. Adverse events within 4 years occurred in 112 (13·2%, 95% CI 11·0–15·6) of 898 patients, with 66 (8·0%, 95% CI 6·2–10·0) arising from 78 untreated non-culprit lesions (mean baseline angiographic diameter stenosis 46·9% [SD 15·9]). Highly lipidic lesions (851 [24%] of 3500 lesions, present in 520 [59%] of 884 patients) were an independent predictor of patient-level non-culprit lesion-related MACEs (adjusted odds ratio 2·27, 95% CI 1·25–4·13) and non-culprit lesion-specific MACEs (7·83, 4·12–14·89). Large plaque burden (787 [22%] of 3629 lesions, present in 530 [59%] of 898 patients) was also an independent predictor of non-culprit lesion-related MACEs. Lesions with both large plaque burden by intravascular ultrasound and large lipid-rich cores by NIRS had a 4-year non-culprit lesion-related MACE rate of 7·0% (95% CI 4·0–10·0). Patients in whom one or more such lesions were identified had a 4-year non-culprit lesion-related MACE rate of 13·2% (95% CI 9·4–17·6). Interpretation: Combined NIRS and intravascular ultrasound detects angiographically non-obstructive lesions with a high lipid content and large plaque burden that are at increased risk for future adverse cardiac outcomes. Funding: Abbott Vascular, Infraredx, and The Medicines Company.