Background The intensive polychemotherapy regimen eBEACOPP (bleomycin, etoposide, doxorubicin, cyclophosphamide, vincristine, procarbazine, and prednisone in escalated doses) is very active in patients with advanced-stage Hodgkin's lymphoma, albeit at the expense of severe toxicities. Individual patients might be cured with less burdensome therapy. We investigated whether metabolic response determined by PET after two cycles of standard regimen eBEACOPP (PET-2) would allow adaption of treatment intensity, increasing it for PET-2-positive patients and reducing it for PET-2-negative patients. Methods In this open-label, randomised, parallel-group phase 3 trial, we recruited patients aged 18–60 years with newly diagnosed, advanced-stage Hodgkin's lymphoma in 301 hospitals and private practices in Germany, Switzerland, Austria, the Netherlands, and the Czech Republic. After central review of PET-2, patients were assigned (1:1) to one of two parallel treatment groups on the basis of their PET-2 result. Patients with positive PET-2 were randomised to receive six additional cycles of either standard eBEACOPP (8 × eBEACOPP in total) or eBEACOPP with rituximab (8 × R-eBEACOPP). Those with negative PET-2 were randomised between standard treatment with six additional cycles of eBEACOPP (8 × eBEACOPP) or experimental treatment with two additional cycles (4 × eBEACOPP). A protocol amendment in June, 2011, introduced a reduction of standard therapy to 6 × eBEACOPP; after this point, patients with positive PET-2 were no longer randomised and were all assigned to receive 6 × eBEACOPP and patients with negative PET-2 were randomly assigned to 6 × eBEACOPP (standard) or 4 × eBEACOPP (experimental). Randomisation was done centrally using the minimisation method including a random component, stratified according to centre, age (<45 vs ≥45 years), stage (IIB, IIIA vs IIIB, IV), international prognostic score (0–2 vs 3–7), and sex. eBEACOPP was given as previously described; rituximab was given intravenously at a dose of 375 mg/m2 (maximum total dose 700 mg). The primary objectives were to show superiority of the experimental treatment in the PET-2-positive cohort, and to show non-inferiority of the experimental treatment in the PET-2-negative cohort in terms of the primary endpoint, progression-free survival. We defined non-inferiority as an absolute difference of 6% in the 5-year progression-free survival estimates. Primary analyses in the PET-2-negative cohort were per protocol; all other analyses were by intention to treat. This trial was registered with ClinicalTrials.gov, number NCT00515554. Findings Between May 14, 2008, and July 18, 2014, we recruited 2101 patients, of whom 137 were found ineligible before randomisation and a further 19 were found ineligible after randomisation. Among 434 randomised patients (217 per arm) with positive PET-2, 5-year progression-free survival was 89·7% (95% CI 85·4–94·0) with eBEACOPP and 88·1% (83·5–92·7) with R-eBEACOPP (log-rank p=0·46). Patients with negative PET-2 randomly assigned to either 8 × eBEACOPP or 6 × eBEACOPP (n=504) or 4 × eBEACOPP (n=501) had 5-year progression-free survival of 90·8% (95% CI 87·9–93·7) and 92·2% (89·4–95·0), respectively (difference 1·4%, 95% CI −2·7 to 5·4). 4 × eBEACOPP was associated with fewer severe infections (40 [8%] of 498 vs 75 [15%] of 502) and organ toxicities (38 [8%] of 498 vs 91 [18%] of 502) than were 8 × eBEACOPP or 6 × eBEACOPP in PET-2-negative patients. Ten treatment-related deaths occurred: four in the PET-2-positive cohort (one [<1%] in the 8 × eBEACOPP group, three [1%] in the 8 × R-eBEACOPP group) and six in the PET-2-negative group (six [1%] in the 8 × eBEACOPP or 6 × eBEACOPP group). Interpretation The favourable outcome of patients treated with eBEACOPP could not be improved by adding rituximab after positive PET-2. PET-2 negativity allows reduction to only four cycles of eBEACOPP without loss of tumour control. PET-2-guided eBEACOPP provides outstanding efficacy for all patients and increases overall survival by reducing treatment-related risks for patients with negative PET-2. We recommend this PET-2-guided treatment strategy for patients with advanced-stage Hodgkin's lymphoma. Funding Deutsche Krebshilfe, Swiss State Secretariat for Education and Research, and Roche Pharma AG.