This study will determine whether a stepwise increase of the drug infliximab (Remicade® (Registered Trademark)) controls juvenile rheumatoid arthritis more effectively than a fixed dose. It will look at the safety and effectiveness of increasing the dose to a maximum of 15mg/kg body weight per dose, examining the drug's effect on bone and cartilage, and whether it can improve abnormal growth, metabolism and hormones. Infliximab is approved for treating adults with rheumatoid arthritis and Crohn's disease.||Children between 4 and 17 years of age with active juvenile rheumatoid arthritis who do not respond adequately to standard therapy may be eligible for this study.||Participants will receive nine infusions of infliximab during this 62-week study. The drug is given intravenously (IV, into a vein) over 2 hours. The first three infusions will be at a dose of 5 mg/kg of body weight. Children who improve on this regimen will receive another 6 infusions at the same dose. Children who do not significantly improve on 5 mg/kg at the end of 6 weeks (the third infusion) may continue with phase 2 of the study, in which they will be randomly assigned to receive either: 1) 6 additional doses of the drug at 5 mg/kg per dose, or 2) a gradually increased dose to a maximum of 15 mg/kg. In addition, all children will continue to take methotrexate at the same dose as when they entered the study.||Participants will visit the NIH Clinical Center 12 times (about every 8 weeks) during the study for the following tests and procedures:||History and physical examination, including a complete joint exam|Puberty assessment - breast development in girls, testicle size in boys, and pubic hair|Height and weight measurements||Children will have imaging studies (x-rays, MRI and Dexa scan) at the beginning and end of the study and will collect a 24-hour urine sample before each infliximab infusion.||Patients may elect to have an endocrine evaluation. This involves Clinical Center hospitalizations for 1-1/2 days on visits 1, 4 and 12. Small amounts of blood will be drawn every 20 minutes (through an indwelling catheter to avoid multiple needle sticks) for 8 hours while the child sleeps. The blood will be examined for the normal rhythm of growth hormone and other substances in the body and how they are affected by arthritis.||Participants will complete a questionnaire once a year for 2 years to provide information on their health status and any problems that might be related to the study drug.