BACKGROUND: Therapeutic hypothermia is standard of care for babies with moderate to severe hypoxic-ischaemic encephalopathy. There is limited evidence to inform provision of nutrition during hypothermia. OBJECTIVES: To assess the association during therapeutic hypothermia between (1) enteral feeding and outcomes, such as necrotising enterocolitis and (2) parenteral nutrition and outcomes, such as late-onset bloodstream infection. DESIGN: A retrospective cohort study using data held in the National Neonatal Research Database and applying propensity score methodology to form matched groups for analysis. SETTING: NHS neonatal units in England, Wales and Scotland. PARTICIPANTS: Babies born at ≥ 36 gestational weeks between 1 January 2010 and 31 December 2017 who received therapeutic hypothermia for 72 hours or who died during treatment. INTERVENTIONS: Enteral feeding analysis - babies who were enterally fed during therapeutic hypothermia (intervention) compared with babies who received no enteral feeds during therapeutic hypothermia (control). Parenteral nutrition analysis - babies who received parenteral nutrition during therapeutic hypothermia (intervention) compared with babies who received no parenteral nutrition during therapeutic hypothermia (control). OUTCOME MEASURES: Primary outcomes were severe and pragmatically defined necrotising enterocolitis (enteral feeding analysis) and late-onset bloodstream infection (parenteral nutrition analysis). Secondary outcomes were survival at neonatal discharge, length of neonatal stay, breastfeeding at discharge, onset of breastfeeding, time to first maternal breast milk, hypoglycaemia, number of days with a central line in situ, duration of parenteral nutrition, time to full enteral feeds and growth. RESULTS: A total of 6030 babies received therapeutic hypothermia. Thirty-one per cent of babies received enteral feeds and 25% received parenteral nutrition. Seven babies (0.1%) were diagnosed with severe necrotising enterocolitis, and further comparative analyses were not conducted on this outcome. A total of 3236 babies were included in the matched enteral feeding analysis. Pragmatically defined necrotising enterocolitis was rare in both groups (0.5% vs. 1.1%) and was lower in babies who were fed during hypothermia (rate difference -0.5%, 95% confidence interval -1.0% to -0.1%; p = 0.03). Higher survival to discharge (96.0% vs. 90.8%, rate difference 5.2%, 95% confidence interval 3.9% to 6.6%; p < 0.001) and higher breastfeeding at discharge (54.6% vs. 46.7%, rate difference 8.0%, 95% confidence interval 5.1% to 10.8%; p < 0.001) rates were observed in enterally fed babies who also had a shorter neonatal stay (mean difference -2.2 days, 95% confidence interval -3.0 to -1.2 days). A total of 2480 babies were included in the matched parenteral nutrition analysis. Higher levels of late-onset bloodstream infection were seen in babies who received parenteral nutrition (0.3% vs. 0.9%, rate difference 0.6%, 95% confidence interval 0.1% to 1.2%; p = 0.03). Survival was lower in babies who did not receive parenteral nutrition (90.0% vs. 93.1%, rate difference 3.1%, 95% confidence interval 1.5% to 4.7%; p < 0.001). LIMITATIONS: Propensity score methodology can address imbalances in observed confounders only. Residual confounding by unmeasured or poorly recorded variables cannot be ruled out. We did not analyse by type or volume of enteral or parenteral nutrition. CONCLUSIONS: Necrotising enterocolitis is rare in babies receiving therapeutic hypothermia, and the introduction of enteral feeding is associated with a lower risk of pragmatically defined necrotising enterocolitis and other beneficial outcomes, including rates of higher survival and breastfeeding at discharge. Receipt of parenteral nutrition during therapeutic hypothermia is associated with a higher rate of late-onset infection but lower mortality. These results support introduction of enteral feeding during therapeutic hypothermia. FUTURE WORK: Randomised trials to assess parenteral nutrition during therapeutic hypothermia. TRIAL REGISTRATION: Current Controlled Trials ISRCTN474042962. FUNDING: This project was funded by the National Institute for Health Research (NIHR) Health Technology Assessment programme and will be published in full in Health Technology Assessment; Vol. 25, No. 36. See the NIHR Journals Library website for further project information.