Freed U.S. hostage David Roeder shouts and waves as he arrives at Rhein-Main U.S. Air Force base in Frankfurt, Germany. Roeder was among 52 Americans held hostage in Iran for 444 days after their capture at the U.S. Embassy in Tehran. January 21, 1981.
Freed U.S. hostage David Roeder shouts and waves as he arrives at Rhein-Main U.S. Air Force base in Frankfurt, Germany. Roeder was among 52 Americans held hostage in Iran for 444 days after their capture at the U.S. Embassy in Tehran. Jan. 21, 1981.AP Photo
Freed U.S. hostage David Roeder shouts and waves as he arrives at Rhein-Main U.S. Air Force base in Frankfurt, Germany. Roeder was among 52 Americans held hostage in Iran for 444 days after their capture at the U.S. Embassy in Tehran. January 21, 1981.
Kathryn Koob, right, and Elizabeth Ann Swift hold hands as they leave the Algerian aircraft which brought them to Algiers from Tehran at Algiers airport, Jan. 21, 1981. The women were two of the United States hostages held for 444 days in Iran.
Outgoing US Deputy Secretary of State, Warren Christopher (right) strolls away under an umbrella, as the American hostages freed from Iran, and Algerian officials, gather around the Algerian aircraft that flew the hostages to freedom at Algiers airport, on Wednesday, Jan. 21, 1981. Christopher, who led the negotiating team, greeted the hostages as they the aircraft.
A group of American hostages give the victory sign as they emerge from an Algerian aircraft in Algiers after their flight from Teheran where they had been held captive for 444 days in Iran, Jan. 21, 1981.
A crowd of well-wishers on the balconies of the Wiesbaden U.S. Air Force hospital greets the 52 Americans released by the Iranian government, January 21, 1981, after being held hostage for 444 days. A sign displayed by a group of people reads, "Welcome to the Freedom Hotel."
Some of the 52 American citizens held hostage in Iran for 14 months are cheered by the crowd at the Wiesbaden U.S. Air Force hospital, after their release in West Germany, Wednesday morning, Jan. 21, 1981.
Former U.S. president Jimmy Carter, who came to Wiesbaden to greet the U.S. hostages released from captivity, embraces one of the former hostages, believed to be Bruce Laingen, Jan. 21, 1981.
Former American hostage John Graves from Reston, Va., shakes hands with people in the crowd at the Rhein-Main U.S. Air Force base in Frankfurt, West Germany on January 21, 1981, shortly before traveling home to the United States.
Freed U.S. hostage David Roeder shouts and waves as he arrives at Rhein-Main U.S. Air Force base in Frankfurt, Germany.
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See 8 Joyous Photos of the Iran Hostages Going Free in 1981

When the dozens of Americans who had been held hostage in Iran for 14 1/2 months were told they'd be going free, they didn't believe it. As TIME reported in a cover package about the incredible confluence of events that took place 35 years ago on Jan. 20, 1981—a date that saw both the hostages released and the inauguration of President Ronald Reagan—an Iranian spokesperson said they "moved about like sleepwalkers."

But their initially muted response made sense, the article explained: "The Americans had been divided by their captors into at least two groups for transportation to the airport in buses with blackened windows. The Americans then were run through a gauntlet of chanting militants. While some hostages thought the dozens of militants forming a corridor to shout 'Death to America!' at them were just performing for propaganda effect, others were genuinely frightened and reported that they had been kicked and shoved during their last steps on Iranian soil."

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It wasn't until they were safely on board an Air Algerie 727, and even then not until they'd waited a half hour to taxi, that the champagne was (literally) popped. After a brief refueling stop in Greece, they flew on to Algiers, landed, and walked down the ramp as free men and women. The following day, the former hostages arrived at Wiesbaden U.S. Air Force hospital in Germany, their final stop before finally going home.

"They flashed victory signs," TIME reported of the scene in Algeria, "and clenched fists and shouted to throngs of spectators: 'Thank you! Thank you! We made it!'"

Read the full cover story about the hostage release, here in the TIME Vault: The Ordeal Ends

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