This 2-arm study will investigate the safety and tolerability of oseltamivir for the treatment of influenza in immunocompromised participants and characterize the effects of oseltamivir in immunocompromised participants on the development of resistant influenza virus. Eligible immunocompromised participants with laboratory-confirmed influenza will be randomized to receive either conventional dose (30 milligrams [mg]-75mg twice daily orally [po], depending on age and weight) or double dose (60mg-150mg twice daily po depending on age and weight) Tamiflu for 10 days. Nasal and throat swabs will be taken, and safety evaluations made, at intervals during the study. The anticipated time on study medication is 10 days and the anticipated time on study is 40 days.