A High Court judge has considered the applications on the papers and adjourned the cases to a hearing in open court. The judge has issued interim injunctions preventing their removal prior to those hearings. The judge has direct the hearings be fixed urgently.
The European Court of Human Rights ruled there was no bar to the extradition of these men.
We will continue working to ensure they are handed over to the US authorities as soon as possible.
A second terror suspect, Khaled Al-Fawwaz, has also mounted a legal challenge.
Radical cleric Abu Hamza has launched a last-minute High Court challenge in a move to avoid extradition to the United States, it was confirmed
The judge presiding over the case of a man accused of ordering the contract killing of his wife has adjourned the case to 18 September to consider psychiatric reports from experts. Shrien Dewani will attend only if well enough.
The Defence and the CPS have asked the judge to consider whether a further adjournment of a year is necessary.
The defence of Shrien Dewani have quoted his psychiatrist today saying that he has made some progress with his mental health, remains on drug treatment and is in compulsory detention in a psyciatric unit until May 2013. Mr Dewani has been accused of ordering his wife's murder on their honeymoon.
With both his mental conditions - a depressive illness and Post Traumatic Stress Disorder - he has moved from a severe to a moderate diagnosis.
He remains at risk of suicide, though this is decreasing. His recovery is slow and they argue that it will be impeded by more court hearings at this time. They say his best prospects of recovery are if there is an adjournment of 12 months.
Mr Dewani remains, according to his psychiatrist, unable to give an account of himself, with his memory loss possibly linked to his PTSD condition.
South African government representative Hugo Keith QC has said today that he wants the case against Shrien Dewani to be adjourned until late September/early October for the South African government to gather further medical evidence on Dewani's condition.
Dewani, 32, denies any involvement in the killing of his wife Anni in Cape Town, in November 2010.
The defence (Clare Montgomery QC) want a longer adjournment, as they say that this presents the best chance of Mr Dewani making a sufficient recovery.
The extradition case of a man accused of ordering his wife's murder on honeymoon is due to resume today.
Shrien Dewani, 32, denies any involvement in the killing of his wife Anni in Cape Town, in November 2010.
South African authorities want him to face allegations of masterminding the murder of his bride during their honeymoon.
The case of computer hacker Gary McKinnon returns to the High Court today.
His mother Janis Sharp has told Daybreak that leading psychiatric experts have already concluded the 46-year-old would be at high risk of committing suicide if removed.
Mr McKinnon admits hacking US military computers but says he was looking for evidence of UFOs.
The United States is pleased with the finding of the European Court of Human Rights regarding defendants Babar Ahmad, Syed Ahsan, Mustafa Kamal Mustafa (Abu Hamza), Adel Bary and Khaled Al-Fawwaz.
We look forward to the court's decision becoming final and to the extradition of these defendants to stand trial in the United States.
With respect to defendant Haroon Rashid Aswat, US officials will consult with the United Kingdom's Home Office about the additional submission requested.