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Summary Background Treatments for small-cell lung cancer (SCLC) after failure of platinum-based chemotherapy are limited. We assessed safety and activity of nivolumab and nivolumab plus ipilimumab in patients with SCLC who progressed after one or more previous regimens. Methods The SCLC cohort of this phase 1/2 multicentre, multi-arm, open-label trial was conducted at 23 sites (academic centres and hospitals) in six countries. Eligible patients were 18 years of age or older, had limited-stage or extensive-stage SCLC, and had disease progression after at least one previous platinum-containing regimen. Patients received nivolumab (3 mg/kg bodyweight intravenously) every 2 weeks (given until disease progression or unacceptable toxicity), or nivolumab plus ipilimumab (1 mg/kg plus 1 mg/kg, 1 mg/kg plus 3 mg/kg, or 3 mg/kg plus 1 mg/kg, intravenously) every 3 weeks for four cycles, followed by nivolumab 3 mg/kg every 2 weeks. Patients were either assigned to nivolumab monotherapy or assessed in a dose-escalating safety phase for the nivolumab/ipilimumab combination beginning at nivolumab 1 mg/kg plus ipilimumab 1 mg/kg. Depending on tolerability, patients were then assigned to nivolumab 1 mg/kg plus ipilimumab 3 mg/kg or nivolumab 3 mg/kg plus ipilimumab 1 mg/kg. The primary endpoint was objective response by investigator assessment. All analyses included patients who were enrolled at least 90 days before database lock. This trial is ongoing; here, we report an interim analysis of the SCLC cohort. This study is registered with ClinicalTrials.gov, number NCT01928394. Findings Between Nov 18, 2013, and July 28, 2015, 216 patients were enrolled and treated (98 with nivolumab 3 mg/kg, three with nivolumab 1 mg/kg plus ipilimumab 1 mg/kg, 61 with nivolumab 1 mg/kg plus ipilimumab 3 mg/kg, and 54 with nivolumab 3 mg/kg plus ipilimumab 1 mg/kg). At database lock on Nov 6, 2015, median follow-up for patients continuing in the study (including those who had died or discontinued treatment) was 198·5 days (IQR 163·0–464·0) for nivolumab 3 mg/kg, 302 days (IQR not calculable) for nivolumab 1 mg/kg plus ipilimumab 1 mg/kg, 361·0 days (273·0–470·0) for nivolumab 1 mg/kg plus ipilimumab 3 mg/kg, and 260·5 days (248·0–288·0) for nivolumab 3 mg/kg plus ipilimumab 1 mg/kg. An objective response was achieved in ten (10%) of 98 patients receiving nivolumab 3 mg/kg, one (33%) of three patients receiving nivolumab 1 mg/kg plus ipilimumab 1 mg/kg, 14 (23%) of 61 receiving nivolumab 1 mg/kg plus ipilimumab 3 mg/kg, and ten (19%) of 54 receiving nivolumab 3 mg/kg plus ipilimumab 1 mg/kg. Grade 3 or 4 treatment-related adverse events occurred in 13 (13%) patients in the nivolumab 3 mg/kg cohort, 18 (30%) in the nivolumab 1 mg/kg plus ipilimumab 3 mg/kg cohort, and ten (19%) in the nivolumab 3 mg/kg plus ipilimumab 1 mg/kg cohort; the most commonly reported grade 3 or 4 treatment-related adverse events were increased lipase (none vs 5 [8%] vs none) and diarrhoea (none vs 3 [5%] vs 1 [2%]). No patients in the nivolumab 1 mg/kg plus ipilimumab 1 mg/kg cohort had a grade 3 or 4 treatment-related adverse event. Six (6%) patients in the nivolumab 3 mg/kg group, seven (11%) in the nivolumab 1 mg/kg plus ipilimumab 3 mg/kg group, and four (7%) in the nivolumab 3 mg/kg plus ipilimumab 1 mg/kg group discontinued treatment due to treatment-related adverse events. Two patients who received nivolumab 1 mg/kg plus ipilimumab 3 mg/kg died from treatment-related adverse events (myasthenia gravis and worsening of renal failure), and one patient who received nivolumab 3 mg/kg plus ipilimumab 1 mg/kg died from treatment-related pneumonitis. Interpretation Nivolumab monotherapy and nivolumab plus ipilimumab showed antitumour activity with durable responses and manageable safety profiles in previously treated patients with SCLC. These data suggest a potential new treatment approach for a population of patients with limited treatment options and support the evaluation of nivolumab and nivolumab plus ipilimumab in phase 3 randomised controlled trials in SCLC. Funding Bristol-Myers Squibb.