The goal of this clinical research study is to learn if dasatinib can help to control myeloproliferative disorders. The safety and tolerability of dasatinib will also be studied.

Dasatinib is an experimental anti-cancer drug that is designed to block the function of BCR-ABL, which is the abnormal protein responsible for causing leukemia in some cells.

If you are found to be eligible to take part in this study, you will take dasatinib by mouth twice a day. If you have mastocytosis, you will take dasatinib by mouth once a day. A treatment cycle will be defined as 4 weeks (28 days) + 7 days. You will be instructed to take dasatinib in the morning (between about 6:00 a.m.-10:00 a.m.) and in the evening (between about 6:00 p.m.-10:00 p.m.).

Blood tests (about 2 - 3 teaspoons) will be done once a week for a month, then once a month for 5 years, then once every 6 months (if your doctor thinks it is needed) for the remainder of your treatment on this study. A bone marrow biopsy will be done after 1-2 months of therapy to document response.

Dasatinib will be given for as long as you are responding. You will be taken off study if the disease gets worse or intolerable side effects occur.

This is an investigational study. Dasatinib is authorized for use in research only. A total of 145 patients will take part in this study. All will be treated at MD Anderson.

Inclusion Criteria:

1. Patients >/= 18 years old who meet the following eligibility criteria
2. Patients must have one of the following hematopoietic malignancies: C-kit positive (10% or more BM or PB MNC positive by flow) acute myeloid leukemia (AML excluding acute promyelocytic leukemia) or myelodysplastic syndrome (MDS) of the following types: Refractory-relapse AML-MDS including those who fail to achieve Complete Response (CR) after the first cycle of induction; Second or subsequent AML-MDS refractory-relapse; Newly diagnosed AML-MDS patients over 60 years of age with karyotype other than t(15:17), inv16, t(8:21), who do not want chemotherapy.
3. (Con't from # 2) Patients with MDS who do not want chemotherapy as initial treatment, or who are not eligible for the treatments of higher priority.
4. Agnogenic myeloid metaplasia - myelofibrosis (MMM)
5. Hypereosinophilic syndrome (HES)
6. Polycythemia vera (PV)
7. Mastocytosis
8. Serum bilirubin less than 2mg%, serum creatinine less than 2mg% unless abnormality is considered due to hematologic malignancy by investigator.
9. Eastern Cooperative Oncology Group (ECOG) Performance Status < 3
10. Patients must sign an informed consent indicating they are aware of the investigational nature of this study, in keeping with the policies of the hospital.
11. Women of pregnancy potential must practice an effective method of birth control during the course of the study, in a manner such that risk of failure is minimized. Prior to study enrollment, women of childbearing potential (WOCBP) (defined as not post-menopausal for 12 months or no previous surgical sterilization) must be advised of the importance of avoiding pregnancy during trial participation and the potential risk factors for an unintentional pregnancy.
12. Continued from #11: In addition, men enrolled on this study should understand the risks to any sexual partner of childbearing potential and should practice an effective method of birth control.Women and men must continue birth control for the duration of the trial and at least 3 months after the last dose of study drug.
13. Inclusion of women and minorities: As per NIH policy, women and members of minorities will be included in this protocol as they are referred in the relevant populations. There are no exclusions of women or minorities based on the study objectives.
14. New York Heart Association (NYHA) Class < 3
15. Ph negative MPD including chronic myelomonocytic leukemia (CMML).

Exclusion Criteria:

1. Pregnant or breast-feeding women are excluded.
2. All WOCBP MUST have a negative pregnancy test prior to first receiving investigational product. If the pregnancy test is positive, the patient must not receive investigational product and must not be enrolled in the study.