Patients in this study will take 4 tablets of imatinib mesylate by mouth every day. Patients with HES will take 1 tablet daily to begin, and may go up to 4 tablets daily depending on response. Imatinib mesylate should be taken each morning at breakfast with a large glass of water. Bottles containing the tablets will be given to the patient every month. Unused supplies must be returned at the end of the study. Patients taking oral hydroxyurea to control their blood counts, can continue it during the first month of imatinib mesylate treatment, but must stop taking it from then on.