The released American hostages are undergoing medical tests in Texas
Relatives of the three US government contractors who were held hostage by left-wing Farc rebels in Colombia, have expressed joy at their homecoming.
Marc Gonsalves, Thomas Howes and Keith Stansell have arrived back in Texas, where they will undergo medical tests and be reunited with their families.
The men were among 15 hostages, including Ingrid Betancourt, rescued by Colombian troops on Wednesday.
They were kidnapped in 2003 after their plane crashed in the Colombian jungle.
The Farc has been fighting to overthrow the Colombian government for 40 years, and Ms Betancourt - a French-Colombian politician - was their highest-profile captive.
Colombian officials said the Farc rebels had been tricked into handing over the hostages by soldiers posing as members of a fictitious non-government organisation.
The Farc still holds more than 40 high-profile hostages, and among up to 700 other captives.
'I missed you'
A plane carrying the US trio landed at about 2315 (0415 GMT) at a military base in San Antonio, Texas, from where they were taken to a military medical facility for tests.
A spokesman for the men's families told the AFP news agency that they "express their gratitude to the soldiers and the Colombian intelligence forces, who risked their lives in this daring operation".
George Gonsalves said he was mowing his lawn when he heard his son Marc had been rescued.
"First thing I want to say to him is, my God, I missed you. I love you. And I want to hug him, and I want to touch him, and I want to hear his voice again," he told CNN.
Kyle Stansell described the moment he learned of his father's release.
"I didn't even know what to do. I just started freaking out - screaming, yelling. I ran as fast as I could off the beach.
"As far as we know, everything's going fine," Mr Stansell told CNN. "I just want to see my dad."
The US government lists the Farc as a terrorist organisation and has refused to negotiate with the group.
The US ambassador to Colombia said there had been "close co-operation" from the Americans in the run-up to the rescue, including sharing of intelligence, equipment and training advice.