Brimelow, who first came to the US on Fulbright Scholarship (and then left again, as required by conditions of that scholarship) has been an American citizen since 1994. Here's his description of that process, from a debate on Dual Citizenship:
Okay, okay, I know it sounds too good to be true. But the question of dual citizenship really was hotly discussed in a crowd of my fellow Americans-to-be as we all waited patiently for the judge to arrive and administer the Oath of Allegiance one summer day back in 1994. The woman behind me reflected the consensus. "Of course!" she forcefully declared to general approval, in the event of another military draft she would send her children back to the Caribbean — which she could do precisely because they all were retaining their original citizenship. While waiting to "swear allegiance"! With court officers all around!
Then the judge arrived. He swore us in and told us we were now as good Americans as anyone whose family had been here 10 generations (translation: you don't have to assimilate), and that the United States still had a major problem: racism (i.e., vote Democratic). Obviously my Caribbean friend knew something I didn't.
Intimate contact with the immigration process is one reason we immigrants usually are so much less romantic about immigration than are American intellectuals and policy wonks.