Computer hacker Gary McKinnon has won his 10-year fight against extradition after the Home Secretary stepped in to halt proceedings.
Abu Qatada's appeal hearing against extradition to Jordan began today.
Radical Islamist cleric Abu Hamza has been flown to the USA after he lost his last-ditch High Court challenge against extradition.
Gary McKinnon's lawyer says she's hopeful the home secretary will reject a bid to extradite him to the US on hacking charges.
She told BBC Radio 4's Today programme: "I am optimistic because David Cameron and Nick Clegg were so vocal in opposition in support of Gary.
"Nick Clegg said he thought it would be morally wrong for Gary to be extradited and David Cameron said it would show no compassion to send Gary to America so I'm really hoping they are going to stand by the promises they made in opposition."
She added: "Theresa May can make a decision that if Gary is at extreme risk of suicide, that she can prevent his extradition and we have provided her with the medical report, which will allow her, within the law, to make that decision."
Computer hacker Gary McKinnon will find out later today whether the Home Secretary Theresa May will halt his extradition to America.
Mr McKinnon, who has Asperger's syndrome, faces trial in the US over hacking into military files over a decade ago.
Some of the evidence put forward against terror suspect Abu Qatada in Jordan has been described as "extremely thin" by senior immigration judge , Mr Justice Mitting.
He is the president of the Special Immigration Appeals Commission, which is considering Mr Qatada's appeal against extradition to Jordan.
The Appeals Commission will test whether sufficient assurances have been received from Jordan to ensure he gets a fair trial - rather than the strength of the case against him.
1999 - Abu Qatada is convicted in his absence on terror charges in Jordan and sentenced to life imprisonment.
2005 - The preacher is arrested under immigration rules as the Government seeks to deport him to Jordan.
2008 - The Court of Appeal rules that deporting him would breach his human rights, because evidence used against him in Jordan may have been obtained through torture.
2009 - Five Law Lords rule that Qatada can be deported, on the basis of assurances from foreign governments that he will get a fair trial.
January 2012 - European judges rule that he cannot be deported while "there remains a real risk that evidence obtained by torture will be used against him", but that diplomatic assurances from Jordan would clear the way for his deportation.
April 2012 - Home Secretary Theresa May secures assurances from Jordan that it will "bend over backwards" to ensure Qatada receives a fair trial. Qatada's legal team lodges a fresh appeal attempt with Europe's human rights judges - but loses the case in May.
August 2012 - Qatada lodges a fresh attempt for freedom at the High Court.
A panel of judges will begin hearing an appeal by Abu Qatada to be freed while he fights extradition to Jordan. The radical cleric has been sentenced in his absence to life imprisonment with hard labour for conspiracy to carry out terror attacks.
His mother Janis Sharp said outside court:
If Theresa May has got an ounce of compassion she would make her decision now before the Olympics because she has any number of medical reports - these delays are destroying my son's life.
The case of computer hacker Gary McKinnon returns to the High Court today.
The hearing follows his refusal last week to undergo further medical tests by a Home Office-appointed expert as he fights extradition to the United States.
The US authorities want McKinnon, from Wood Green, north London, to face trial for hacking into military computers 10 years ago.