They populate Odessa's numerous terrace cafés, stroll in hordes through its parks, and fill the plush velvet seats of its 19thcentury opera house. A foreign man, usually though not always over 60 and American, sits with a Ukrainian girl, probably in her twenties and strikingly attractive. Habitually, they are joined by another young woman, the translator, who facilitates the dialogue.

"She says she likes a strong man who knows his mind." "Tell her I love the idea of two cultures coming together in a relationship." "She says she thinks you could be her soulmate."

Hundreds of dating agencies operate in Odessa, luring the foreign dollar into the laidback Black Sea port city with a suggestion of the nubile young model living a life so impoverished that she will be ready to fly away with the first slack-skinned foreign pensioner who offers her a way out. Other cities in Ukraine, and other countries in Eastern Europe and Asia, also have well-developed bride industries, but Odessa is a global hub for men looking for love.

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Curious to find out if the "mail-order bride" is alive and well in the 21st century, I joined a 10-day "romance tour" organised by Anastasia Date, one of the world's biggest "international dating" agencies. The company had £90m of revenue last year, mainly through its prodigiously expensive chat services, where men pay up to £1 per minute to talk with women located across the globe, or up to £10 to send them an email message. As a by-product, the company runs tours to locations as diverse as Colombia, the Philippines, and Ukraine, to meet the women they have met online.

For the not inconsequential sum of £3,000, the 39 men present at our induction meeting on day one have bought the chance to attend three "socials" – huge events at nightclubs where they will be in the company of hundreds of young Ukrainian women apparently looking for love. They then have a week to go on dates with the women they encounter at the socials, meet up with those they have met online previously, and perhaps end their tour with a proposal.

With their clipboards and information packs, the men listen attentively to the induction speech in our hotel's conference room, given by tour leader John Carlton, who speaks in a Tennessee drawl. Most of the "ladies" do not speak English, and thus the men will require the services of the red-shirted translators who will also be present at the social, he tells us. Amid the US contingent, there are also two Brits, a smattering of Europeans, and a Saudi. Some of the Americans wear sharp suits and talk loudly about their property empires; others are from small towns in the Midwest and have acquired passports specially to make the trip. Most of the men are divorced and in their fifties or sixties. The oldest is 76-year-old Giuseppe, an Italian plastic surgeon, while the youngest is 29-year-old Chris, a stand-up comic from New York. With an outgoing personality and a full set of teeth, I wondered what he was doing on the tour.

"I realised something earlier than these guys," he says, as the group journeys across Odessa on a testosterone-filled bus to the first social. "Western women are not – how do I put this politely – family oriented. I was with a girl who just stole $3,500 from me and disappeared, changed her phone number. There is a lot of selfishness in American women. They have no values." It is a complaint I will hear from almost all the men during my week in Odessa. Divorced and disenchanted at 29, Chris has made the journey half way round the world to Ukraine in search of a strange combination of these lost "family values" – and sex. "A friend came on one of these trips and said it was like Disneyland for anyone with a penis," he says. "I want to go to Penis Disneyland!"

We arrive at the nightclub and leave the warm spring sunshine for its dingy interior. Chris wears a tuxedo and top hat; others wear stiff suits and ties; Darren, from a small town in North Dakota, wears a shellsuit. Inside, dozens of women await, enjoying a free glass of champagne and branded with white stickers bearing their "ID number". The men take in a panoramic vista of leopard print, stilettos and carefully plumped cleavage. Some of them immediately begin their chat-up routines; others look nervous. For one of them, I find out later, it is not only his first trip outside the US, but also the first time he has ever been to a nightclub.

"I'm very conservative, so I never go to bars or clubs," says 47-year-old Joe, a hay farmer from Pennsylvania with an awkward manner. Affable but shy, Joe has trouble meeting women at home, and has had little contact with women since his wife died of cancer five years ago. "I've tried local dating sites but nobody wants to live on a farm," he says. "I wrote to one lady and said she had nice hair, but she didn't even reply to say thank you." Faced with so many women to choose from at the social, he had no idea where to start. "The first half an hour, I just clammed up. I am not used to being outgoing, or talking to ladies, so I didn't know what to do." Others find it easier: within half an hour, Mohammed from Saudi Arabia has his arms around two women and is throatily growling "Nothing Else Matters" by Metallica on a karaoke system.

The socials spawn dozens of dates for the coming week, but there is a recurring complaint among the men. Most have spent between £3,000 and £10,000 chatting to women online prior to the tour, and were looking forward to meeting in person these women with whom they had formed an emotional connection. But when they arrived in Odessa, in the vast majority of cases, the women were nowhere to be seen. Some of them turned off their phones, others arranged dates but did not arrive. Many had been called away at the last minute to tend to an ailing relative. The men were distraught. Darren from North Dakota had 10 women lined up that he had been chatting with; he met just a couple of them in person. It was a similar story with many of the others.

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There was much consternation about the flakiness of Ukrainian women. When the dates did show up, many of the men were reporting extraordinarily expensive evenings.f For a start, even when the men suspect that their dates speak perfect English, they are forced into taking translators, who require payment by the hour. Todd from Delaware, a bread-delivery man who had worked seven night-shifts per week for the past six months to be able to afford the trip, has been taken to a pool club where the bill came to £250. Chris has been taken for an overpriced meal and thinks he saw the waiter give his date a kickback after he had paid the bill. He is beginning to wonder whether Ukrainian women might be just as bad as their American counterparts. "They have vaginas, and vaginas lie," he says, despairingly.

It becomes clear that the dating scene in Odessa is not all it seems. Locals laugh when I ask them about the strange no-shows, and tell me that in all probability, the women that these men thought they were falling in love with do not even exist. Everyone I speak to seems to have a sister or a friend who is involved in writing fake letters and engaging in online chats with foreigners. People are reluctant to go into details, but finally I find Alina, who agrees to show me how it works. We meet at a café in a distant, shabby suburb of Odessa, far from the handsome buildings and cobbled streets of the centre. "Two months ago I applied for translation work, but it turned out what they needed was someone to actually write fake messages. I despise it, it makes me feel sick, but I have no other source of income," she says. Showing me how the scam works seems to be her way of assuaging her conscience. Alina is a slight 25-year-old brunette, but on the dating site she chats as Inessa – a leggy, busty, 21-year-old blonde. Inessa really exists – it required her passport for her to register on the website. But she has a boyfriend and wants nothing to do with it, she simply got a free professional photoshoot for signing up; the pictures are now being used to lure Western men on to the website.

Alina spends hours every week online, pretending to be Inessa. For every minute she chats, she receives £0.08. She shows me an inbox full of love letters to Inessa from Americans, Australians, Brits. Alina says many of her friends also have fake accounts on the site. Alina's sister has her real photos on her profile, but is not interested in meeting a foreign man; she has a serious boyfriend. Instead, the chats are her main source of income. If the men ever actually show up in Odessa, Alina's sister takes them out on a series of overpriced non-sexual "dates", receiving kickbacks in each venue, and her husband acts as their "taxi driver", taking an enormous fare from the man at the end of each day.

I ask a representative of Anastasia, which owns the biggest chat website and is running my tour, about the fake accounts, and he insisted that the company has a "zero tolerance policy" towards fake accounts and engages in regular checks. The company also points to a litany of success stories of Western-Ukrainian partnerships that have ended in marital bliss. It is clear that men do occasionally find Ukrainian wives, but hardly anyone on my tour appears to have found love. The days of lonely Texans flying into Odessa, picking up a bride, and flying out with her are long gone, it seems.

"Everything is possible; there are women who genuinely want to meet a man and emigrate," says a foreigner living in Odessa who is well acquainted with the dating industry. "In the villages there are even more of them. But there are very few of them in Odessa, these days. Especially those who would be willing to marry a man in his sixties or seventies. They love Odessa, and they can make good money scamming these idiots. Why would they actually go through with it and move to some boring place in rural America?"

Armed with what I have found out, I view the men's stories each evening over beers at the hotel in a different light. I am particularly worried about Stephen, a 62-year-old Texan oil worker who has bought a ring and plans to propose to his 27-year-old pianist "girlfriend", who bears a passing resemblance to Cameron Diaz. He made his decision after one date, when he took her bowling and she told him (via the translator) that she thought she could be his "soulmate".

Stephen's world view and gender values are alien to me, and he occasionally says shocking things. "The thing I really like about her is that both of her parents are dead," he tells me one evening. "So she would probably miss home less." But despite all this, I find it difficult to watch him at the bar every evening, making plans for romantic weekends, or a costumed visit to the Texas Renaissance Festival ("It's one of the largest in the country!") with his new Ukrainian wife.

"She'll say yes to his proposal, milk him for money for 'English lessons' for the next six months, and then disappear," predicts Alina, when I tell her about Stephen. When he complains to me of the vast sums he is forking out every day for the translator fees, taxi rides, and gifts of Swarovski jewellery, I make gentle suggestions that perhaps all is not what it seems. I smile weakly when he talks of plans to redecorate his house ahead of the arrival of his new wife, and I wonder if I should sit him down and set him to rights. But he is old enough to work things out for himself. I leave him the day before his departure on the way to a karaoke bar, where he plans to propose.

On the penultimate night of the tour, a group of the men without pressing dates goes to Palladium, one of Odessa's top nightclubs. Go-go dancers with their backs to the dancefloor make thrusting movements with rock-hard, oiled buttocks, as the men look on with a mixture of awe and confusion. "I haven't been to a place like this for 30 years," says Brian, a dishevelled British solicitor in his fifties, dressed for a Tuesday in the office and casting a beady eye over the pulsating dancefloor. He plans to return in a fortnight, and might propose to his new "girlfriend", a 27-year old blonde model. "Perhaps it's all a pack of lies. I don't know. But I'll be a few hundred quid down if it is. And maybe I'll come back with a beautiful young wife. It's a gamble worth taking."

Indeed, as the tour winds down, even those men who were sent to the depths of despair by dates who did not show up, fleeced them, or led them on, are planning return trips to Ukraine. Some have already been more than once; one of them is on his 14th tour. For some of them, merely the fleeting hope of happiness seems to be enough, while others hold on to a conviction that next time it might just be different. It strikes me that the men have the logic of compulsive gamblers after an unsuccessful trip to a casino. They have played, they have lost, and they know that the chances of success are minimal, but they continue throwing money at it in the vague hope that maybe they will be the one for whom the right cards come up.

The day after the tour ends, I receive an email from Chris. On the final night he decided to go on a date with one of the women from the socials. As she spoke no English, the usual translator, with the standard hourly rate, also came along. He was determined to get her and her translator drunk, and find out the truth about dating in Odessa. "After several drinks my date miraculously learnt almost fluent English, and we debated how women here take financial advantage of the men that come on these tours," he wrote. She told him that the men are effectively paying to sit at a restaurant with a beautiful woman. If they are naïve enough to think there is a romantic attachment, then that is their problem.

"I have come to the conclusion that there are no victims in Odessa," Chris writes. "Only two opposing cons, both trying to get as much as they can out of each other."

Some of the names in this story have been changed