Wikileaks founder Julian Assange will find out next week if he is to be extradited to Sweden to faces sex crime allegations.
Lawyers for Assange had asked the UK's highest court to block the move, claiming the European arrest warrant issued against was "invalid and unenforceable".
A panel of seven Supreme Court judges, who heard the case in February, will give their judgment next Wednesday.
The Swedish authorities want Assange, 40, to answer accusations of raping one woman and sexually molesting and coercing another in Stockholm in August 2010 while on a visit to give a lecture.
Assange, whose WikiLeaks website has published a mass of leaked diplomatic cables that embarrassed several governments and international businesses, says the sex was consensual and the allegations against him are politically motivated.
In November 2011, the High Court upheld a ruling by District Judge Howard Riddle - who sat at Belmarsh Magistrates' Court, south London, in February 2011 - that the Australian computer expert should be extradited to face investigation.
If the Supreme Court rejects his appeal it will mark the end of his lengthy legal battle in the UK, but it will still be open to him to ask the European Court of Human Rights in Strasbourg to intervene.
Special arrangements are being made by the Supreme Court because of the worldwide interest of press and media in the judgment.
The High Court declared that it would not be unfair or unlawful to extradite Assange. But his QC argued in the Supreme Court that the Swedish public prosecutor who signed the arrest warrant could not issue a valid document because she lacked impartiality and independence.
Assange, who is on bail living with friends, attended the two-day hearing in person and is likely to be back for next week's crucial ruling.