Intergroup Randomized Trial for Children or Adolescents With B-Cell Non Hodgkin Lymphoma or B-Acute Leukemia: Rituximab Evaluation in High Risk Patients

Inclusion Criteria: * Histologically or cytologically proven B-cell malignancies, either Burkitt lymphoma or B-AL (=Burkitt leukaemia = L3-AL) or diffuse large B-cell NHL or aggressive mature B-cell NHL non other specified or specifiable. * Stage III with elevated LDH level ("B-high"), \[LDH \> twice the institutional upper limit of the adult normal values (\> Nx2)\] or any stage IV or B-AL. * 6 months to less than 18 years of age at the time of consent. * 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, MALT and nodular marginal zone are not included into this therapeutic study * Patients with congenital immunodeficiency, chromosomal breakage syndrome, prior organ transplantation, previous malignancy of any type, or known positive 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 during less than one week. * Tumor cell negative for CD20 * Prior exposure to rituximab. * Severe active viral infection, especially hepatitis B. * Hepatitis B carrier status history of HBV or positive serology. * Participation in another investigational drug clinical trial. * Patients who, for any reason, are not able to comply with the national legislation.