A Muslim convert who lost his British citizenship three years ago is claiming he has been left stateless, which is illegal under international law.
The 31-year-old man, identified only as 'B2', has been taking legal action against Home Secretary Theresa May who stripped him of his British citizenship in December 2011 because of alleged extremism.
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B2, who was born in Vietnam, came to the UK with his parents when he was 12 years old and acquired British nationality.
He then allegedly became a follower of terrorist group AQAP (Al-Qaeda in the Arabian Peninsula), which has been accused of a number of bomb plots and attempts to recruit followers from the West. The security services said he became an "Islamist extremist" and received terrorist training at the group's base in Yemen in 2010.
The Home Secretary has the power to remove someone's British citizenship if they have another nationality, explains the BBC. B2's appeal has partly rested on whether or not he has retained his Vietnamese citizenship under Vietnamese law.
Last year, the Court of Appeal decided that he had retained his Vietnamese nationality, despite the Vietnamese government apparently rejecting him as one of its citizens without going through any of its own legal procedures.
The Supreme Court hearing comes ahead of a Parliamentary debate about counter-terrorism proposals that would allow the Home Secretary to ban British jihadist suspects from returning to the UK.