The three U.S. military contractors - Marc Gonsalves, Thomas Howes and Keith Stansell - had been held by the Revolutionary Armed Forces of Colombia since their drug-surveillance plane went down in the jungle in February 2003.
They were among 15 hostages, including former Colombian presidential candidate Ingrid Betancourt and 11 members of the Colombian security services, rescued by Colombian forces in a daring mission Wednesday.
"I will tell you that they greeted me with a strong handshake and clear eyes and an incredible smile," said Maj. Gen. Keith Huber, commanding general of U.S. Army South, which is responsible for Army operations in Latin America and the Caribbean.
The men, employees of a Northrop Grumman Corp. subsidiary, arrived in the U.S. late Wednesday. They were then taken to Brooke Army Medical Center at San Antonio's Fort Sam Houston to undergo tests.
Eric Atkisson, a spokesman for U.S. Army South, said the former hostages would not speak publicly Thursday.
The men's families were arriving in San Antonio throughout the day, said Katie Lamb, a Northrop Grumman spokeswoman. Stansell had already seen his son Kyle and daughter Lauren, as well as his father and stepmother, Huber said.
"So on the tail end of their first private reunion in five years and five months, I can tell you that it made us all very proud that there were children there who were thrilled to see their parent and there were parents there who were overwhelmed with seeing their son back safe," Huber said.
He said Howes - whose birthday is Friday - and Gonsalves were also to reunite with their families Thursday.
The men are undergoing what Huber said is a reintegration process and are in the second phase, which typically lasts two to four days, he said.
"The purpose is to provide a transition back to normal life after the strains of captivity," Huber said.
He said the men's participation in the process is voluntary because they are not members of the military.
Asked about possible disease, Col. Jackie Hayes, the hospital's chief of pulmonary and critical care, would not discuss specific conditions the men might have.
Hayes said that as of now, the men aren't believed to have any infectious or communicable diseases.
U.S. Ambassador William Brownfield had said Wednesday that two of the three men were suffering from the jungle malady leishmaniasis, which is caused by parasites, and were "looking forward to modern medical treatment."
Kelly Coady, Stansell's ex-wife, told The Associated Press by phone from Sarasota, Fla., that Stansell spent an hour with 16-year-old Kyle and 19-year-old Lauren.
"Kyle said his father looked really good, looked thin, but looked really, really good," Coady said, adding that Stansell was "amazed at how much bigger Kyle was than him."
Mike Gonsalves said Thursday that the news of his brother's rescue was starting to feel more real.
"He looks good," Gonsalves, of Manchester, Conn., told CBS' "Early Show" in a phone interview before going to Texas. "They all look, you know, good for being what they went through - I think they look pretty good."
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