WASHINGTON — A military appeals court on Wednesday overturned the terrorism conviction of an Australian whose guilty plea was once hailed as a sign that the tribunal system at the Guantánamo Bay, Cuba, prison would be swift and effective.

That prediction proved to be wrong. The system has endured a decade of fits, starts and do-overs. With its decision on Wednesday, the Court of Military Commission Review threw out the conviction of the Australian, David Hicks, who trained with Al Qaeda and whose case was one of the tribunal system’s few successes.

Mr. Hicks had pleaded guilty to a charge of providing material support to a terrorist organization, but the court found that was not considered a war crime at the time of the plea and was not eligible to be heard at Guantánamo. The Pentagon has acknowledged that to be the case, but the Obama administration argued that Mr. Hicks was technically not eligible to appeal the conviction. The court disagreed.

Mr. Hicks, who was sentenced to nine months in prison in 2007, has been living in Australia for years. The court’s decision will remove the terrorism conviction from Mr. Hicks’s record.