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."
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