The goal of this clinical research study is to see if Pegasys (IFN-alpha2a) can help to control the disease in patients with ET, PV, AMM/MF, and Ph-negative CML. The safety of this treatment will also be studied.

IFN-alpha2a has been used for the treatment of a variety of disorders (such as hepatitis C). IFN-alpha2a is a drug that may affect the way infections and malignant diseases develop.

Before treatment starts, you will have blood (around 2 teaspoons) and bone marrow samples collected. To collect a bone marrow sample, an area of the hip or chest bone is numbed with anesthetic and a small amount of bone marrow is withdrawn through a large needle. These samples will be used for tests to confirm the diagnosis of the disease. Women who are able to have children must have a negative blood pregnancy test.

During treatment, you will receive IFN-alpha2a as an injection under the skin once a week. You (or your caregiver) will be taught how to give the injections, and you will receive treatment on an outpatient basis.

Treatment will continue (injections once a week) as long as the disease does not get worse.

If the disease gets worse or you experience any intolerable side effects, you will be taken off the study and your doctor will discuss other treatment options with you.

During treatment you will have blood (around 1 teaspoon) collected every other week for 2 months, then once every 1 or 2 months for a year, then every 3 months. You will also have bone marrow samples collected every 3 to 6 months during the first year of treatment. After the first year of treatment, bone marrow samples will be collected only when your doctor feels they are needed. The blood and bone marrow samples will be used for tests to check on the response to therapy.

This is an investigational study. IFN-alpha2a has been approved by the FDA for the treatment of hepatitis C and is commercially available. However the use of IFN-alpha2a in this study is investigational. The commercial prepartion of IFN-alpha2a(Pegasys) will be used in this study. Up to 280 participants will take part in this study. All will be enrolled at M. D. Anderson.

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 </= 2 (ECOG scale).
3. Age greater than 18 years since disease is extremely rare in younger age group.
4. Adequate liver function: total bilirubin of </= 2.0 mg/dl (except for patients with 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 </= 2.0 mg/dl).
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.