However, they weren't all American, and they weren't all just after one thing.
Jessie Daigle, who is now 90 and lives in Abbeyhill, met a handsome Canadian serviceman, Fernand, in Edinburgh's Palais de Danse dancehall in 1942, and by the time the war was out they were married.
She says: "He was a handsome, strapping man when I met him. My husband was in the Army, and was later shipped off to France to take part in the D-Day landings."
After the war there were about 100 Canadian war brides, and about the same number of children, who were shipped off to Canada to be reunited with their husbands.
"We shipped out in a convoy and it took us 10 days to reach Canada, arriving in the port of Halifax.
"It wasn't very pleasant spending 10 days on a crowded boat with 100 women and 100 screaming children, but we got there in the end.
"I was heading on to Montreal, where my husband's family lived, and it took me another 24 hours to get there by train.
"My husband didn't come home for quite a while after the war, so I lived with his family in Montreal.
"They were very kind, and they made me fell very welcome.
"I stayed in Canada for the next 30 years, until my husband died in 1976 and then I came back to Edinburgh.
"One of my children still lives over there, and I still go over every year for a visit."
However, Jessie recalls that not all relationships with foreign servicemen proved to be quite so fruitful.
She says: "Some of the girls used to line up at Waverley Station and choose their men. They were just like everyone said with loads of cash and a supply of nylons, which you couldn't get in those days.
"However, the girls knew a secret that the men didn't. If they met up with their men and they turned out to be an idiot, or if they didn't like them, they used to say: 'I'm just nipping off to the toilet', but there was a back door leading out of the toilets at Waverley Station.
"You used to see these lines of women escaping out the back, leaving the poor guy waiting there for her to come out. It was quite funny, really!"