BACKGROUND: The International Extranodal Lymphoma Study Group-32 (IELSG32) trial is an international randomised phase 2 study that addresses two key clinical questions in the treatment of patients with newly diagnosed primary CNS lymphoma. Results of the first randomisation have demonstrated that methotrexate, cytarabine, thiotepa, and rituximab (called the MATRix regimen) is the induction combination associated with significantly better outcome compared with the other induction combinations tested. Here, we report the results of the second randomisation that addresses the efficacy of myeloablative chemotherapy supported by autologous stem-cell transplantation (ASCT), as an alternative to whole-brain radiotherapy (WBRT), as consolidation after high-dose-methotrexate-based chemoimmunotherapy. METHODS: HIV-negative patients (aged 18-70 years) with newly diagnosed primary CNS lymphoma and an Eastern Cooperative Oncology Group performance status of 0-3 were randomly assigned to receive four courses of methotrexate 3.5 g/m(2) on day 1 plus cytarabine 2 g/m(2) twice daily on days 2 and 3 (group A); or the same combination plus two doses of rituximab 375 mg/m(2) on days -5 and 0 (group B); or the same methotrexate-cytarabine-rituximab combination plus thiotepa 30 mg/m(2) on day 4 (group C), with the three groups repeating treatment every 3 weeks. Patients with responsive or stable disease after induction treatment, with adequate autologous peripheral blood stem-cell collection, and without persistent iatrogenic side-effects, were eligible for the second randomisation between WBRT (photons of 4-10 MeV; five fractions per week; fraction size 180 cGy; started within 4 weeks from the last induction course; group D) and carmustine-thiotepa conditioned ASCT (carmustine 400 mg/m(2) on day -6, and thiotepa 5 mg/kg every 12 h on days -5 and -4, followed by reinfusion of autologous peripheral blood stem cells; group E). A permuted block randomised design was adopted for both randomisations, and a computer-generated randomisation list was used within each stratum. No masking after assignment to intervention was adopted. The primary endpoint was 2-year progression-free survival, with induction group and response to induction chemotherapy as stratification parameters. Analyses were done on a modified intention-to-treat basis. This study is registered with ClinicalTrials.gov, number NCT01011920. FINDINGS: Between Feb 19, 2010, and Aug 27, 2014, 227 patients were recruited from 53 centres in five countries. 219 of 227 enrolled patients were assessable. Of the 122 patients eligible for the second randomisation, 118 patients were randomly assigned to WBRT or ASCT (59 patients per group) and constitute the study population. WBRT and ASCT were both effective, and achieved the predetermined efficacy threshold of at least 40 progression-free survivors at 2 years among the first 52 patients in both groups D and E. There were no significant differences in 2-year progression-free survival between WBRT and ASCT: 80% (95% CI 70-90) in group D and 69% (59-79) in group E (hazard ratio 1.50, 95% CI 0.83-2.71; p=0.17). Both consolidation therapies were well tolerated. Grade 4 non-haematological toxicity was uncommon; as expected, haematological toxicity was more common in patients treated with ASCT than in those who received WBRT. Two toxic deaths (infections) were recorded, both in patients who received ASCT. INTERPRETATION: WBRT and ASCT are both feasible and effective as consolidation therapies after high-dose methotrexate-based chemoimmunotherapy in patients aged 70 years or younger with primary CNS lymphoma. The risks and implications of cognitive impairment after WBRT should be considered at the time of therapeutic decision. FUNDING: Agenzia Italiana del Farmaco, Cancer Research UK, Oncosuisse, and Swiss National Science Foundation.