summarily execute them as spies
send them to an American tribunal for adjudication
treat them as prisoners of war despite not being in uniform
hand them over to the authorities of whatever nation they are captured in
send them for "rendition" in an allied nation
"A nation can survive its fools, and even the ambitious. But it cannot survive treason from within. An enemy at the gates is less formidable, for he is known and carries his banner openly. But the traitor moves amongst those within the gate freely, his sly whispers rustling through all the alleys, heard in the very halls of government itself. For the traitor appears not a traitor; he speaks in accents familiar to his victims, and he wears their face and their arguments, he appeals to the baseness that lies deep in the hearts of all men. He rots the soul of a nation, he works secretly and unknown in the night to undermine the pillars of the city, he infects the body politic so that it can no longer resist. A murder is less to fear"
Cicero Marcus Tullius
They should be trialed for treason.
Nevertheless, the warmongering mental vomit (i. e. "NUKE EM LETS GO BLOW EM UP AND SPEND US TAXPAYER DOLLARS ON TEN WARS THERE HELL YEAH!!!) from the right-wing and Libertarian-wannabes is typical, and expected.
Quo usque tandem abutere, Trump, patientia nostra?
Unfortunately, due to the voting of habits of the mentally deficient right, whose craniums have been permanently bolted up Limbaugh's anus, we have pols who can't tell the difference between the two.
I believe under a certain amount of different circumstances here's what should happen.
1) If they are American citizens only and are captured on the battlefield, they should be returned to the United States where they must face trial under military law for treason where should crimes against humanity/murder be determined to have been committed against civilians by that individual, the death penalty would be administered. Otherwise life in imprisonment.
1.5) They should already have had their passport nullified, I don't know what the lawful process would be for removing an Americans citizenship for fighting against the state or if that's even possible but should they attempt to return to the US of their own free will they should be detained immediately and 1) is followed.
2) If they are captured and hold dual citizenship with another nation, they should be turned over to that nations jurisdiction and their American citizenship subsequently revoked. If that nation will not have them than 1) is followed.
Permanently revoke their American citizenship. If they are caught in the US, send them to Syria or Iran or Saudi Arabia (payback to the Saudis), take their US passports and revoke their US citizenship. To me it would be a fate worse than death.
"When Faith preaches Hate, Blessed are the Doubters." - Amin Maalouf