The study evaluates the efficacy and tolerability of alternating short cycles of high-dose and conventional chemotherapy in combination with rituximab in CD20 positive patients, followed by local radiation therapy in the case of initial mediastinal or central nervous system (CNS) involvement or a residual tumor after chemotherapy. A dose-reduced regimen is offered for patients estimated to be over 55 years, biologically.

Inclusion Criteria:

• Burkitt's leukemia or Burkitt's lymphoma or primary mediastinal large B-cell lymphoma or B-precursor lymphoblastic lymphoma or large cell anaplastic lymphoma
• Age > 15 years
• Written informed consent

Exclusion Criteria:

• Serious secondary diseases, including psychiatric conditions, under which the required therapy compliance is not to be expected
• HIV infection
• Secondary lymphoma following prior chemotherapy/radiotherapy or active second malignancy
• Known severe allergy to foreign proteins
• Pre-treatment other than 1 cycle CHOP or similar; < 1 week of another chemotherapy.
• Pregnancy or nursing
• Participation in other studies that interfere with study therapy