Background: Patients with relapsed or refractory B-cell non-Hodgkin lymphoma have few treatment options. We aimed to establish the safety and recommended phase 2 dose of epcoritamab, a novel bispecific antibody that targets CD3 and CD20 and induces T-cell-mediated cytotoxic activity against CD20+ malignant B cells. Methods: For the dose-escalation part of this phase 1/2 study, we enrolled adults (aged ≥18 years) with relapsed or refractory CD20+ B-cell non-Hodgkin lymphoma at ten sites across four countries (Denmark, the Netherlands, the UK, and Spain). Eligible patients received priming and intermediate doses followed by full doses of subcutaneous epcoritamab administered in 28-day cycles; each subsequent cohort involved escalation of the priming, intermediate, or full dose (0·0128–60 mg). The primary objectives were to determine the maximum tolerated dose and the recommended phase 2 dose. Safety, antitumour activity, pharmacokinetics, and immune biomarkers were also assessed. This study is registered with ClinicalTrials.gov, NCT03625037, with the dose-expansion part ongoing. Findings: Between June 26, 2018, and July 14, 2020, we enrolled 73 patients with relapsed, progressive, or refractory CD20+ mature B-cell non-Hodgkin lymphoma. 68 patients received escalating full doses (0·0128–60 mg) of subcutaneous epcoritamab. No dose-limiting toxic effects were observed, and the maximum tolerated dose was not reached; the full dose of 48 mg was identified as the recommended phase 2 dose. All 68 patients received at least one dose of epcoritamab and were included in safety analyses: common adverse events were pyrexia (47 patients [69%]), primarily associated with cytokine release syndrome (CRS; 40 [59%], all grade 1–2), and injection site reactions (32 [47%]; 31 grade 1). There were no grade 3 or higher CRS events. No discontinuations occurred due to treatment-related adverse events or treatment-related deaths. Overall response rate in patients with relapsed or refractory diffuse large B-cell lymphoma was 68% (95% CI 45–86), with 45% achieving a complete response at full doses of 12–60 mg. At 48 mg, the overall response rate was 88% (47–100), with 38% achieving a complete response. Patients with relapsed or refractory follicular lymphoma had an overall response rate of 90% (55–100), with 50% achieving a complete response at full doses of 0·76–48 mg. Epcoritamab induced robust and sustained B-cell depletion, and CD4+ and CD8+ T-cell activation and expansion, with modest increases in cytokine levels. Interpretation: Single-agent subcutaneous epcoritamab for treatment of patients with relapsed or refractory B-cell non-Hodgkin lymphoma merits investigation in ongoing phase 2 and phase 3 studies. Funding: Genmab and AbbVie.