Twenty to thirty percent of children with epilepsy continue to suffer from seizures, even when treated with currently available anticonvulsant medications. Children with Lennox-Gastaut Syndrome (LGS) are particularly handicapped by atonic-myoclonic seizures. Preliminary data suggest that even when other medications have failed, these seizures may respond rapidly and dramatically to a high-fat-low-carbohydrate ketogenic diet. The purpose of the study is to assess if the classic ketogenic diet is efficacious in reducing seizure frequency, medication toxicity, and improves quality of life.