A Muslim convert, stripped of his British citizenship because of alleged extremism, is appealing to the Supreme Court that he has been left stateless.
The man, only identified as "B2", lost his British citizenship in 2011.
The home secretary used nationality powers to withdraw his citizenship because of his alleged activity.
Supreme Court justices must decide whether the man was left without any nationality, which is illegal under international law.
The hearing comes ahead of Parliament debating controversial counter-terrorism proposals that would allow the Home Secretary to ban British nationals from returning to the UK when they are thought to have been involved in terrorism overseas.
Home Secretary Theresa May has long-standing powers to strip someone of their British nationality when the individual has another citizenship.
In this unusual case, B2 was born in Vietnam and came to the UK when he was 12 years old with his parents.
Six years later, they were granted British nationality. B2 studied design and communications at college and when he was 21, converted to Islam.
The home secretary's security case against him is that he became a follower of al-Qaeda in the Arabian Peninsula (AQAP) and in 2010 went to its base in Yemen, then run by an influential American-Yemeni preacher, Anwar al-Awlaki.
AQAP followers have been behind a number of bomb plots and produced Inspire, an English-language jihadist magazine, which was designed and presented to attract more recruits from the West.
by Clive Coleman, BBC legal affairs correspondent
B2's case represents legal scrutiny of another aspect of the government's range of measures to deal with those suspected of involvement in terrorism.
Last week the prime minister announced plans to bar suspected British jihadist fighters from re-entering the UK unless they agreed to strict terms.
The announcement of these temporary exclusion orders which could last up to two years led to a debate about the legality of those orders, and of any measures that render a UK citizen "stateless".
B2's case raises the issue of the home secretary's power to deprive naturalised UK citizens of citizenship when another government disowns them - as the Vietnamese government has done in B2's case.
The British government claims that the Vietnamese decision to disown B2 is wrong in Vietnamese law.
So the Supreme Court will decide if citizens in B2's position are rendered stateless when a foreign government has disowned them "unlawfully".
It will also consider whether B2, as a national of a nation of the EU, can be deprived of his EU citizenship - and whether it is proportionate to do so if no other state recognizes him as a citizen.
In December 2011, Mrs May made an order stripping B2 of his nationality, saying that he was involved in terrorist-related activity.
Court papers say that MI5 had assessed he posed an "active threat to the safety and security of the UK and its inhabitants".
Two days later, Mrs May served a second order that he be deported to Vietnam and he was placed in detention.
The Vietnamese government deny that B2 is one of its citizens. But the British government says the Vietnamese have got their own law wrong - and therefore B2 is not stateless.
B2 appealed against his loss of citizenship to the Special Immigration Appeals Commission, a semi-secret court that deals with cases involving national security, saying he had been left stateless.
The Siac panel agreed - but the Home Secretary later won an appeal after arguing that Vietnamese government had got its own law wrong in denying that B2 was one of its citizens.
After ministers initially lost this case and another similar challenge, the government asked Parliament to amend the law, so that the home secretary could rescind someone's citizenship if officials believed that person could turn to another nationality, even if they did not possess it at the time that they lost their British status.
The Supreme Court hearing in the case is expected to last two days with a judgement coming later.