WASHINGTON — Within the next few days, possibly as early as Thursday, the Supreme Court will announce how it plans to handle one of the most daunting logistical challenges in the court's recent history: organizing and scheduling the appeals in the massive campaign-finance case in a manner most likely to produce a coherent presentation and prompt decision.

It has been just over a month since a special three-judge U.S. District Court here issued its 1,638-page ruling that upheld some parts and struck down others of the new campaign-finance law. In that time, a dozen separate appeals have been submitted to the Supreme Court, which under a special provision of the law is required to accept the case and to hear it on an expedited basis.

The justices will devote part of their private weekly conference on Thursday to considering various proposals for meeting the requirement of speed. A mid-summer argument, once considered a possibility, no longer appears to be an option, but the court might well decide to hear the case in September rather than wait for the formal start of the new term on Oct. 6.

The Bush administration has proposed several alternatives: shortly after Labor Day, the last week in September, or the week of Oct. 6. The district court issued a stay of its decision, so the law remains in effect until the Supreme Court rules.

The 12 appeals speak for the approximately 80 separate organizations and individuals who participated in the lower court as challengers to or defenders of the new law. The appeals seek the justices' review of some 20 separate issues including, most prominently, the constitutionality of the law's restrictions on the use of soft money — unlimited contributions — by national and state political parties and the ban on the use of money from corporate and labor union treasuries for broadcast advertisements deemed to be "electioneering communications."

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Even the description of 80 parties in 12 appeals raising 20 separate issues understates the complexity of the case as a matter for the Supreme Court's consideration. With the judges on the district court having upheld some provisions and struck down others, everyone is appealing parts of the judgment and defending other parts.

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