This study will evaluate the safety and effectiveness of imatinib mesylate in reducing the number of eosinophils (a type of white blood cell) in patients with hypereosinophilic syndrome (HES). Patients with HES have elevated counts of eosinophils in the blood and body tissues, which can cause damage to these tissues. Although HES can involve any tissues, the heart, nerves, and skin are most often affected. Several drugs, including steroids, interferon, and hydroxyurea can lower eosinophil counts; however, these drugs have drawbacks in that they do not work in all patients with HES, or they may work only temporarily, or patients may develop side effects that require stopping the drugs. Imatinib mesylate is a new drug approved to treat gastrointestinal tumors and chronic myelogenous leukemia. Some data suggest that imatinib mesylate may be useful in treating a subgroup of patients with HES.