Inclusion Criteria:

• Histologically or cytologically proven B-cell malignancies; either Burkitt leukemia or B-AL (= Burkitt leukemia = L3-AL), or diffuse large B-cell NHL, or aggressive mature B-cell NHL non otherwise specified or specifiable (phase III)

  • Stage III with elevated LDH level (B-high) (LDH > twice the institutional upper limit of the adult normal values [> Nx2]), any stage IV, or B-AL (phase III)

• Histolo-cytologically proven PMLBL (phase II)

  • PMLBL without central nervous system (CNS) involvement
  • Slides will be reviewed by the national pathology panel, but review is not mandatory before registration
• Males and females of reproductive potential must agree to use an effective contraceptive method during the treatment, and after the end of treatment: during twelve months for women, taking into account the characteristics of rituximab and during five months for men, taking into account the characteristics of methotrexate
• Complete initial work-up within 8 days prior to treatment that allows definite staging
• Able to comply with scheduled follow-up and with management of toxicity
• Signed informed consent from patients and/or their parents or legal guardians

Exclusion Criteria:

• Follicular lymphoma, Mucosa-Associated Lymphoid Tissue (MALT) and nodular marginal zone are not included into this therapeutic study
• In phase II study (PMLBL) patients with CNS involvement are not eligible
• Patients with congenital immunodeficiency, chromosomal breakage syndrome, prior organ transplantation, previous malignancy of any type, or known positive human immunodeficiency virus (HIV) serology
• Evidence of pregnancy or lactation period
• There will be no exclusion criteria based on organ function
• Past or current anti-cancer treatment except corticosteroids of less than 7 days duration in total
• Tumor cell negative for cluster of differentiation (CD)20 (absence of result due to technical problems in the presence of other characteristics suggestive of BL/DLBCL, including genetic and phenotypic features, is not an exclusion criteria)
• Prior exposure to rituximab
• Severe active viral infection, especially hepatitis B; severe infection (such as sepsis, pneumonia, etc.) should be clinically controlled at the time of randomization; contact the national co-investigator for further advice if necessary

• Hepatitis B carrier status history of hepatitis B virus (HBV) or positive serology; a patient is considered as HBV carrier or to have (had) HBV infection in case of:

  • Unimmunized and hepatitis B surface antigen (HBsAg) and/or anti-HBs antibody and/or anti- HBc antibody positive,

  • Immunized and HBsAG and/or anti-HBc antibody positive

    • Important note: for the phase III trial, a patient without a known history of hepatitis B could be randomized in the study if the serology results are not available at the time of the randomization; however, if the serology results are positive or not available at day 6 (the first day would be due to receive rituximab, if so randomized), the patient must be withdrawn from the study whatever the allocated treatment arm; the data center must be informed immediately; for the phase II trial, the hepatitis B serology results must be available before registration; in each case indicating a carrier status or history for hepatitis B infection, the patients must not receive rituximab, and therefore must not be included in the rituximab trials on any treatment arm; in case of high-risk patients, the recommendation is to treat these patients with the standard LMB regimen corresponding to the patient prognostic group; in the case of PMLBL the physician is left to choose the most appropriate therapy
• Participation in another investigational drug clinical trial
• Patients who, for any reason, are not able to comply with the national legislation