Thousands of children were fathered by American servicemen during the Vietnam war. Now in their 60s and 70s, some veterans are desperate to find the sons and daughters they have never known.

A tall, thin American wearing a straw hat wanders through the narrow streets of Ho Chi Minh City, clutching a photo album. At his side is a Vietnamese interpreter and fixer, Hung Phan, who has helped dozens of former American soldiers locate their long-lost children over the last 20 years. His latest client, the American under the straw hat, is Jerry Quinn. He has come to Vietnam to find his son.

"I know we lived at number 40," says Quinn, looking down the street for the house he used to share with his Vietnamese girlfriend. But there is no number 40.

A small crowd gathers. An elderly man, emerging from his house, explains that when the Vietcong entered Saigon in 1975, they didn't stop at changing the name of the city to Ho Chi Minh City - they also changed all the street names, and even the numbers.

I suppose I am here out of guilt - and to try and do my duty as a father Jerry Quinn

Jerry Quinn is one of two million American soldiers sent to support the South Vietnamese army in the war against the North. During that conflict, it's thought about 100,000 children were born from relationships between local women and American soldiers. Those soldiers are now getting old, and some are guilt-ridden, or just curious to find out what happened to their children.

"But some fathers just don't want to know," says Brian Hjort. Together with Hung Phan, he runs Fathers Founded, a not-for-profit organisation that puts fathers together with their "Amerasian" children. Hjort, a Dane, was just another European backpacker travelling through Vietnam in the 1980s when he came across the Amerasian children. "They were in the street, begging for food and for help," he recalls. "The Vietnamese treated them cruelly - they were the children of the enemy."

Some had photos and knew the names of their fathers. Since the US Government keeps meticulous records of soldiers and veterans, Hjort was soon able to link dozens of children with their fathers - but he was sometimes horrified by the response he received.

Image caption Jerry and his girlfriend, Brandy, before they were parted

"They would yell at me: 'Why are you calling? What do you want? Why are you talking about Vietnam? I don't want to have anything to do with that bastard. He's not my son. She's not my daughter. Stop calling me!'"

But Jerry Quinn, a missionary who lives and works in Taiwan, is anxious to find his son. He says that when he was sent to work in the Far East, he thought it was God's way of telling him to make amends for the past. "I suppose I am here out of guilt," he says. "And to try and do my duty as a father."

Vietnam war timeline Image copyright Getty Images 1954: Vietnam is split into North and South at Geneva conference

1957: Beginning of Communist insurgency in the South

1962: Number of US military advisors in South Vietnam rises to 12,000

1963: Diem overthrown and killed in US-backed military coup

1964: US Congress approves military action in region.

1968: Tet Offensive - combined assault by Viet Cong and North Vietnamese army on US positions - begins

1970: Talks between US and Vietnam begin in Paris

1973: Ceasefire agreement in Paris, US troop pull-out completed by March

1975: North Vietnamese troops invade South Vietnam and take control of the whole country

In 1973, his Vietnamese girlfriend, Brandy, was pregnant and they were negotiating their way through the bureaucracy required to get married. But at the same time, US Secretary of State Henry Kissinger was negotiating a "peace with honour" with the North Vietnamese leaders. The final agreement demanded that US troops leave immediately and Jerry Quinn found himself on a plane home.

"I tried to keep in touch," he says. "I sent her a hundred bucks every month for a year. I never knew whether she got it." Brandy sent him three photos which, 40 years later, he shows to everyone he meets in the streets of Ho Chi Minh City. There are three pictures. A portrait of Brandy, a tall, beautiful Vietnamese girl in her 20s; a picture of her with their baby boy; and a picture of her standing next to a woman in a white coat.

By his third day in the city, Jerry is getting desperate. He and Hung Phan ask for help from the owner of a noodle bar close to the house where Jerry and Brandy once lived together. The owner sits on a stool, turning the pages of the photo album, and when she gets to the picture of Brandy and the woman in the white coat, she stops. "She was the midwife around here," she says. "She now lives in America but they haven't forgotten us and they sometimes come back to visit. In fact her daughter popped in for a bowl of noodles yesterday." Jerry begs the owner to get in touch with the woman, and she obliges.

Kim arrives the next day. An elegant middle-aged woman, she is staying in a smart hotel in the centre of Ho Chi Minh City with her Californian doctor husband. She takes the album, points a perfectly manicured finger at the photo of Brandy and calls out in excitement: "I remember her! We were good friends and I helped deliver your baby."

Kim identifies Brandy's Vietnamese name on the back of one of the photos - Bui. But she can't help Jerry discover his son's first name. When the Vietcong entered the city, she explains, they threatened to kill all those who had had any association with the enemy. "My mother made a huge bonfire and burned everything that might associate us with America." All the carefully kept records of the births were destroyed.

Image caption Jerry and Kim

Choking back tears, Jerry asks Kim if he can hold her hands "because these hands held my baby and this is as close as I may ever get to my son". And there the story might have ended - in a little noodle bar in Vietnam with the customers looking on in amazement, chopsticks suspended in mid-air at the sight of a middle-aged, weeping American holding hands with the woman they know as the midwife's daughter.

More from the Magazine Image copyright AP More than 30 years after being stripped, bound and paraded through countless Vietnamese villages, Pete Peterson returned to the country as America's ambassador. While there, he shook the hands of his captors - and began a mission to save the lives of young swimmers. The ex-POW teaching Vietnam to swim

But Jerry posts the photos of Brandy and the baby to Facebook, and says he is looking for a 40-year-old called Bui, and 8,500 miles away, in Albuquerque, New Mexico, a 40-year-old man called Gary Bui recognises the photos.

Jerry flies to Albuquerque. In the taxi to Gary's house he is shaking with nerves and last-minute doubts. "Will he accept me?" he wonders. "It's been 40 years that he has been waiting for a father. Will he let me hold him? He told me on the phone that he has taught himself not to show emotion."

The taxi pulls up at the house and the family is already outside, waiting for Jerry. "If you looked more like me, you would be me!" he says as he stumbles out of the taxi and grabs his son. They hang on to each other for an age, slapping each other's backs and crying. Looking on are Jerry's two newly-discovered grandchildren.

Slowly, Gary's story emerges. Brandy, like so many mothers of the children of American GIs, abandoned her baby son and fled for her life as Vietcong troops hunted down the women and children of the enemy. The baby was entrusted to friends who took him out of Saigon to hide until the witch-hunt calmed down.

"We lived in the jungle, in clay huts," Gary says. "There was never enough to eat." He was bullied by the other kids, who called his mother a whore. When he was four, he was taken to an orphanage, and four years later he found himself on board a flight to New York as part of a programme launched by the US Government to airlift thousands of Amerasian children to America. Brought up by foster parents, Gary kept copies of the same photos that Brandy had sent Jerry.

Media playback is unsupported on your device Media caption Jerry finally meets his son, Gary

Jerry is wracked by guilt. "I didn't know you were an orphan," he says. "I always thought you would have been with your mother. There is so much I need to learn about you."

Gary's wife and children watch this scene warily. What is there to say to this sudden father-in-law and grandfather, so desperate to know them and love them?

"I know it is late, but I want to be there for you," says Jerry. "I want to be in your life."

Sue Lloyd Roberts' report was broadcast on Newsnight, BBC Two at 22:30 BST on 28 April, and will be broadcast on Our World on BBC News Channel on 3 May at 21:30 - or catch up on BBC iPlayer

Follow @BBCNewsMagazine on Twitter and on Facebook