This NIMH sponsored study is being done to determine the safety and efficacy of a selective serotonin reuptake inhibitor (SSRI), fluoxetine (Prozac), compared to placebo in the treatment of children and adolescents with bipolar disorder who, while taking a mood stabilizer, are currently experiencing an episode of major depression. Bipolar disorder is a recurrent, episodic illness with key features of severe mood swings from one extreme (depression) to the other extreme (mania). These mood swings and associated symptoms are not similar to the normal mood changes that individuals experience from time to time. A person suffering from bipolar disorder, while in an episode of depression or mania, experiences problems in their functioning in several different areas in his or her life such as interpersonal, social, academic and occupational. Symptoms of depression include sad or irritable mood, sleep and appetite disturbances, trouble concentrating, inability to enjoy things that are normally fun, feelings of guilt, low self-esteem, withdrawal from family and friends, suicidal ideation. Symptoms of mania include extremely happy or irritable mood, little need for sleep, poor judgment, continuous high energy, overconfidence, racing thoughts, increase in social interactions, frequent or constant thoughts about sex. There are varying degrees and types of bipolar disorder.