The purpose of this study is to learn how to treat influenza in children less than 2 years of age. Tamiflu®, the drug being studied, is approved for treatment of children 1 year of age and older with influenza. Researchers want to learn more about the activity of Tamiflu® in the body to determine a dose of that is safe, well-tolerated, and effective in young children with influenza. Children less than 24 months of age with confirmed influenza will receive Tamiflu® 2 times a day for 5 days. Older participants will be enrolled first and younger children will be enrolled after the safety data is reviewed for older participants. Study procedures include blood samples, swabs from inside the nose, and body and nervous system evaluations. Participants may be involved in study related procedures for up to 37 days.