Fluoxetine has been approved by the Food and Drug Administration (FDA) for treatment of depression, bulimia, and obsessive-compulsive disorder in adults, but not in children or adolescents. Previous research has shown that fluoxetine is an effective treatment for periods of depression, however, in this study the investigators are evaluating whether it is effective for periods of depression associated with bipolar disorders. In this study, about 100 children and adolescents (ages 8-18 years) who are taking lithium carbonate or valproate (Depakote) and are experiencing depression will be randomized to receive fluoxetine (Prozac) or placebo for 12 weeks. Weekly visits to the clinic are necessary for participation to ensure safety. At the end of the 12 weeks there is an 18-week open treatment period, which will involve clinic visits at least monthly. Those who were taking fluoxetine and improved will continue taking the fluoxetine during this time period. Those who did not improve will either receive an increased dose of fluoxetine or will be assigned to a different medication. Those who were taking placebo and did not improve will be offered treatment with fluoxetine and those who improved with placebo will continue taking only lithium or valproate.