An analysis of statutory procedures proposed in the early 1980s, and which continue to arise, that would allow federal litigants to challenge, on a peremptory basis, the federal judge or magistrate judge assigned to their case. Prepared at the request of the Judicial Conference Advisory Committee on Criminal Rules, the report discusses the proposals that have been offered on the federal level, analyzes the procedures then in effect in seventeen state court systems, and considers the possible administrative consequences of a federal peremptory challenge procedure.