This is a randomized, multi-center, open-label, parallel group study with three arms:

• Rasburicase alone
• Rasburicase followed by Allopurinol
• Allopurinol alone

The primary objective is to compare the adequacy of control of plasma uric acid concentration and the safety profile among the three arms.

After signing the informed consent and having met the inclusion criteria, patients will be randomized to 1 of the 3 arms and treated for a total duration of 5 days. Patients in all arms will receive chemotherapy beginning 4-24 hours after the first dose of rasburicase or allopurinol.

Inclusion Criteria:

1. Meets high risk or at potential risk for tumor lysis syndrome (TLS):

   A patient is at high risk for TLS if he/she presents with:

   • Hyperuricemia of malignancy (plasma uric acid > 7.5 mg/dL);
   • A diagnosis of very aggressive lymphoma/leukemia based on the Revised European-American Lymphoma (REAL) classification of lymphoma/leukemia;
   • Acute myeloid leukemia (AML);
   • Chronic myeloid leukemia (CML) in blast crisis; or
   • High grade myelodysplastic syndrome (refractory anemia with excess blast, chronic myelomonocytic leukemia, and refractory anemia with excess blast in transformation) only if they have > 10% bone marrow blast involvement and are given aggressive treatment similar to AML.

   A patient is at potential risk for TLS if he/she presents with:

   • A diagnosis of aggressive lymphoma/leukemia based on the REAL classification of lymphoma/leukemia plus 1 or more of the following criteria:

     • Lactate dehydrogenase (LDH) >= 2 x upper limit of normal (ULN) (IU/L)
     • Stage III-IV disease
     • Stage I-II disease with at least 1 lymph node/tumor > 5 cm in diameter

   In addition to the above-mentioned eligibility criteria, the patients should have the following criteria:

2. Eastern Cooperative Oncology Group (ECOG) performance status 0-3

3. Age >= 18 years

4. Life expectancy > 3 months

5. Negative pregnancy test (females of child bearing potential) and use of effective contraceptive method (for both males and females). A pregnancy test may be performed on serum or urine human chorionic gonadotropin (HCG).

6. Signed written informed consent