1. Efficacy: To evaluate the effectiveness of rituximab in severe or refractory pediatric ITP, with response defined as follows: platelet count greater than or equal to 50,000/mL on four consecutive weekly measures beginning anytime in weeks 9 - 12 (day 57 - day 84), with the first and fourth measure being spaced at least 22 days apart (i.e., once established during the 9 - 12 week timeframe, the response would be defined as beginning at the first one of these measures). All measurements must be independent of supportive care, as follows: 1) no IVIG (intravenous immunoglobulin) administration within 7 days of the first measure or at any time between measures, 2) no initiation of a 4-day corticosteroid "pulse" within 7 days of the first measure or at any time between measures, 3) no RHo (D) immunoglobulin (WinRHo-SDFTM ) administration within 7 days of the first measure or at any time between measures, and 4) no platelet transfusions administered within 7 days of the first measure or at any time between measures.