The men, aged 39 and 55, were picked up by officers from Scotland Yard's counter terrorism command.
Both are being held under the Extradition Act after being arrested at a residential address in west London.
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Deputy party leader Tom Watson said that what has happened with Jeremy Corbyn is a "great tragedy".
A father who must give police 24 hours' notice before he has sex is planning to go on hunger strike in protest at the "extreme" order.
Remaining unsettled over the next few days.