Inclusion Criteria:

1. Following diagnoses: --ET: Patients with PLT > 600 x10 9 /l documented in the past 12
months; hyperplasia of marrow megakaryocytes in the absence of identifiable cause of
thrombocytosis and in the absence of Ph chromosome. Patients with ET and lower PLT
will be eligible if attributable to prior ET therapy. --PV: Patients should have Hb
>/= 15g/dl (except if patient is having phlebotomies done) and documented past
diagnosis.

2. Performance status
3. Age greater than 18 years since disease is extremely rare in younger age group.

4. Adequate liver function: total bilirubin of Gilbert's Syndrome) and AST (SGOT) or ALT (SGPT) < 3 X ULN (or < 5 X ULN if
considered due to tumor), and renal function (serum creatinine
5. Signed informed consent indicating that patients are aware of the investigational
nature of this study in keeping with the policies of the M.D. Anderson Cancer Center.
The only acceptable consent form is the one approved by the M.D. Anderson Cancer
Center IRB.

6. Willingness and ability to comply with the requirements of the protocol for the
duration of the study.

7. Patients must have been off chemotherapy for 1 week prior to beginning Pegasys and
have recovered from the toxic effects of that therapy. Patients may have received
hydroxyurea or anagrelide immediately before study entry, and may continue into
therapy if treating physician determines this is in the best interest of the patient.

Exclusion Criteria:

1. Pregnant or lactating women.

2. Patients with prior history of another malignancy or concurrent malignancy, except
for the following: basal cell carcinoma of the skin, carcinoma in situ of the cervix,
or other malignancies if the patient is disease free >3 years.

3. Patients with history of ischemic retinopathy.

4. Patients with history of severe cardiac disease: NYHA Functional Class III or IV,
myocardial infarction within 6 months, uncontrolled ventricular tachyarrhythmias or
unstable angina.

5. Patients with history of medically significant psychiatric disease if not controlled,
especially endogenous depression (does not include reactive depression post-cancer
diagnosis), psychosis and bipolar disease.

6. Patients with seizure disorders requiring anticonvulsant therapy.

7. Patients with known infection with HBV, HIV, or other active systemic infection.

8. Patients with known autoimmune disease except for rheumatoid arthritis.

9. Patients with renal disease on hemodialysis.

10. Patients taking continuous or chronic high-dose systemic steroids; if discontinued,
there must be a minimum washout period of one month before study drug is begun.

11. Patients with known hypersensitivity to PEG-IFN alpha-2a or its components.