Attorneys for self-confessed hacker Gary McKinnon have asked the High Court to consider whether home secretary Jacqui Smith was within her rights to refuse a plea to stay McKinnon's extradition to the US to face hacking charges.
The application for a judicial review, sent late last week, asked for either a written decision or an oral hearing before the full court.
Smith previously rejected Kaim Todner's request for McKinnon to face trial in the UK for allegedly hacking more than 73,000 computers belonging to the US Army, Navy and Department of Defense.
Kaim Todner had asked for McKinnon's extradition to be set aside on the grounds that he suffered from Asperger's Syndrome, an autistic condition.
Karen Todner, McKinnon's attorney, said she is appealing Smith's rejection. She expected a response from the court within six to eight weeks.
The former home secretary, John Reid, granted the US a request to extradite McKinnon on 4 July 2006. McKinnon has since appealed and lost in every court available to him, including the European Court of Human Rights.
McKinnon admitted he gained illegal entry to various US military computers between 1999 and 2003, but denied the extent of his alleged incursions or that he caused any monetary damage to the systems.
He claimed he was searching for evidence of UFOs and alien energy creation technology that he believed the US government was suppressing.
The home office declined to comment.