Patients enrolled in the study will take imatinib mesylate daily. Any other drugs they may be taking for HES, as well as other drugs they are taking that may interact with imatinib mesylate, will be tapered and stopped. If it is not possible to stop taking certain drugs for other conditions, their dosages may be adjusted. Patients will be monitored weekly with laboratory testing during the first month of treatment and whenever neutrophil counts drop below 1500/mm3 or platelets fall below 100,000/mm3. If blood counts remain high enough, monitoring will be reduced to every 2 weeks for 3 months and once a month after that. Patients will have a clinic visit at NIH 1 month after beginning the drug for a clinical and laboratory evaluation, including a repeat bone marrow examination. Patients whose eosinophil counts are not lowered after 4 weeks of treatment will leave the study. Those who respond to therapy will return to NIH every 3 months for a history and physical examination, laboratory tests, EKG, echocardiogram, and pulmonary function testing to determine how treatment is affecting disease progression. In some participants with stable disease where an optimal dose of imatinib mesylate has been identified, visits may be extended to every six months. In addition, the following procedures will be done solely for research purposes: