Autism is a developmental disorder that can cause severe and pervasive impairment in thinking, feeling, language, and the ability to relate to others. It is usually first diagnosed in early childhood. Children with autism demonstrate repetitive behaviors or interests and deficits in social interaction, verbal communication, and nonverbal communication. In addition, they often have unusual responses to sensory experiences, such as certain sounds or the way objects look. Some symptoms of attention deficit hyperactivity disorder (ADHD), such as inattention, hyperactivity, and impulsivity, are also associated with autism. Atomoxetine is a selective norepinephrine reuptake inhibitor that is used to treat ADHD. It works differently, however, than stimulant drugs and may help to reduce ADHD symptoms in children with autism. This study will evaluate the effectiveness of atomoxetine in treating children with ADHD symptoms associated with autism.