PD-L1 and CTLA-4 immune checkpoints inhibit antitumour T-cell activity. Combination treatment with the anti-PD-L1 antibody durvalumab and the anti-CTLA-4 antibody tremelimumab might provide greater antitumour activity than either drug alone. We aimed to assess durvalumab plus tremelimumab in patients with advanced squamous or non-squamous non-small cell lung cancer (NSCLC). We did a multicentre, non-randomised, open-label, phase 1b study at five cancer centres in the USA. We enrolled immunotherapy-naive patients aged 18 years or older with confirmed locally advanced or metastatic NSCLC. We gave patients durvalumab in doses of 3 mg/kg, 10 mg/kg, 15 mg/kg, or 20 mg/kg every 4 weeks, or 10 mg/kg every 2 weeks, and tremelimumab in doses of 1 mg/kg, 3 mg/kg, or 10 mg/kg every 4 weeks for six doses then every 12 weeks for three doses. The primary endpoint of the dose-escalation phase was safety. Safety analyses were based on the as-treated population. The dose-expansion phase of the study is ongoing. This study is registered with ClinicalTrials.gov, number NCT02000947. Between Oct 28, 2013, and April 1, 2015, 102 patients were enrolled into the dose-escalation phase and received treatment. At the time of this analysis (June 1, 2015), median follow-up was 18·8 weeks (IQR 11-33). The maximum tolerated dose was exceeded in the cohort receiving durvalumab 20 mg/kg every 4 weeks plus tremelimumab 3 mg/kg, with two (30%) of six patients having a dose-limiting toxicity (one grade 3 increased aspartate aminotransferase and alanine aminotransferase and one grade 4 increased lipase). The most frequent treatment-related grade 3 and 4 adverse events were diarrhoea (11 [11%]), colitis (nine [9%]), and increased lipase (eight [8%]). Discontinuations attributable to treatment-related adverse events occurred in 29 (28%) of 102 patients. Treatment-related serious adverse events occurred in 37 (36%) of 102 patients. 22 patients died during the study, and three deaths were related to treatment. The treatment-related deaths were due to complications arising from myasthenia gravis (durvalumab 10 mg/kg every 4 weeks plus tremelimumab 1 mg/kg), pericardial effusion (durvalumab 20 mg/kg every 4 weeks plus tremelimumab 1 mg/kg), and neuromuscular disorder (durvalumab 20 mg/kg every 4 weeks plus tremelimumab 3 mg/kg). Evidence of clinical activity was noted both in patients with PD-L1-positive tumours and in those with PD-L1-negative tumours. Investigator-reported confirmed objective responses were achieved by six (23%, 95% CI 9-44) of 26 patients in the combined tremelimumab 1 mg/kg cohort, comprising two (22%, 95% CI 3-60) of nine patients with PD-L1-positive tumours and four (29%, 95% CI 8-58) of 14 patients with PD-L1-negative tumours, including those with no PD-L1 staining (four [40%, 95% CI 12-74] of ten patients). Durvalumab 20 mg/kg every 4 weeks plus tremelimumab 1 mg/kg showed a manageable tolerability profile, with antitumour activity irrespective of PD-L1 status, and was selected as the dose for phase 3 studies, which are ongoing. MedImmune.