BACKGROUND: Non-invasive ventilation (NIV) and oxygen therapy (high-flow nasal oxygen [HFNO] or standard oxygen) following extubation have never been compared in critically ill patients with obesity. We aimed to compare NIV (alternating with HFNO or standard oxygen) and oxygen therapy (HFNO or standard oxygen) following extubation of critically ill patients with obesity. METHODS: In this multicentre, parallel group, pragmatic randomised controlled trial, conducted in 39 intensive care units in France, critically ill patients with obesity undergoing extubation were randomly assigned (1:1) to either the NIV group or the oxygen therapy group. Two randomisations were performed: first, randomisation to either NIV or oxygen therapy, and second, randomisation to either HFNO or standard oxygen (also 1:1), which was nested within the first randomisation. Blinding of the randomisation was not possible, but the statistician was masked to group assignment. The primary outcome was treatment failure within 3 days after extubation, a composite of reintubation for mechanical ventilation, switch to the other study treatment, or premature discontinuation of study treatment. The primary outcome was analysed by intention to treat. Effect of medical and surgical status was assessed. The reintubation within 3 days was analysed by intention to treat and after a post-hoc crossover analysis. This study is registered with ClinicalTrials.gov, number NCT04014920. FINDINGS: From Oct 2, 2019, to July 17, 2021, of the 1650 screened patients, 981 were enrolled. Treatment failure occurred in 66 (13·5%) of 490 patients in the NIV group and in 130 (26·5%) of 491 patients in the oxygen-therapy group (relative risk 0·43; 95% CI 0·31-0·60, p<0·0001). Medical or surgical status did not modify the effect of NIV group on the treatment-failure rate. Reintubation within 3 days after extubation was similar in the non-invasive ventilation group and in the oxygen therapy group in the intention-to-treat analysis (48 (10%) of 490 patients and 59 (12%) of 491 patients, p=0·26) and lower in the NIV group than in the oxygen-therapy group in the post-hoc cross-over (51 (9%) of 560 patients and 56 (13%) of 421 patients, p=0·037) analysis. No severe adverse events were reported. INTERPRETATION: Among critically ill adults with obesity undergoing extubation, the use of NIV was effective to reduce treatment-failure within 3 days. Our results are relevant to clinical practice, supporting the use of NIV after extubation of critically ill patients with obesity. However, most of the difference in the primary outcome was due to patients in the oxygen therapy group switching to NIV, and more evidence is needed to conclude that an NIV strategy leads to improved patient-centred outcomes. FUNDING: French Ministry of Health.