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There are concerns that such funds are wiping out the benefits which international debt relief was supposed to bring to poor countries.
Martin Kalunga-Banda, Zambian presidential adviser and a consultant to Oxfam told Newsnight, "That $40m is equal to the value of all the debt relief we received last year."
Vulture funds - as defined by the International Monetary Fund and Gordon Brown amongst others - are companies which buy up the debt of poor nations cheaply when it is about to be written off and then sue for the full value of the debt plus interest - which might be ten times what they paid for it.
Caroline Pearce from the Jubilee Debt campaign told Newsnight it makes a mockery of all the work done by governments to write off the debts of the poorest.
"Profiteering doesn't get any more cynical than this. Zambia has been planning to spend the money released from debt cancellation on much-needed nurses, teachers and infrastructure: this is what debt cancellation is intended for not to line the pockets of businessmen based in rich countries."
In 1979 the Romanian government lent Zambia money to buy Romanian tractors. Zambia was unable to keep up the payments and in 1999 Romania and Zambia negotiated to liquidate the debt for $3m.
Before the deal could be finalised one of Debt Advisory International's vulture funds stepped in and bought the debt from Romania for less than $4m. They are now suing the Zambian government for the original debt plus interest which they calculate at over $40m and they expect to win.
Like the other vulture funds Debt Advisory International refuse to do interviews but reporter Greg Palast caught up with the company founder Michael Sheehan outside his home in Virginia.
Michael Sheehan: "No comment I'm in litigation. It's not my debt."
Greg Palast: Aren't you just profiteering from the work of good people who are trying to save lives by cutting the debt of these poor nations?
Michael Sheehan: Well there was a proposal for investment. That's all I can talk about right now.
Five years ago Gordon Brown told the United Nations that the vulture funds were perverse and immoral: "We particularly condemn the perversity where Vulture Funds purchase debt at a reduced price and make a profit from suing the debtor country to recover the full amount owed - a morally outrageous outcome". But the vulture funds are still operating.
'We don't do interviews'
The London case is just one of many which are running around the world.
Newsnight went to New York to try to interview Paul Singer - the reclusive billionaire who virtually invented vulture funds.
In 1996 his company they paid $11m for some discounted Peruvian debt and then threatened to bankrupt the country unless they paid $58m. They got their $58m.
Now they're suing Congo Brazzaville for $400m for a debt they bought for $10m.
We didn't get our interview. His spokesman told us, "We have nothing to hide; we just don't do interviews".
| || Jubilee Debt Campaign told Newsnight that they are calling on Gordon Brown to turn his moral outrage about vulture funds into action |
Debt Advisory International are very generous to their lobbyists in Washington. They have been paying $240,000 a year to the lobby firm Greenberg Traurig - although recently they jumped ship to another firm after Greenberg Traurig's top lobbyist was put in jail.
Paul Singer has more direct political connections. He was the biggest donor to George Bush and the Republican cause in New York City - giving $1.7m since Bush started his first presidential campaign.
Rudi Guiliani is the favourite to be the next Republican presidential candidate and a leaked memo from his campaign shows that Paul Singer has pledged to raise $15m for Guiliani's campaign.
The vulture funds have teams of lawyers combing the world for assets which can be seized to settle their claims. There have also been claims of dubious tactics.
Back in Britain the Zambian case has seen much legal discussion about allegations of bribery. The Zambian legal team - led by William Blair QC - Tony Blair's brother, has argued that a $2m bribe was offered to the former Zambian President to make it easier for the vulture funds to claim their money.
They showed the court an email disclosed in the Zambia case saying that a payment to the "President's favourite charity" had allowed them to do a more favourable deal.
When we caught up with Michael Sheehan outside his house in Virginia he told us it was not a bribe but a charitable donation.
He told us, "We offered to donate debt to a low income housing initiative which was a charitable initiative which did end up building several thousand houses" before adding "you're contorting the facts, you're on my property and I would ask you to step off".
The Jubilee Debt Campaign told Newsnight that they are calling on Gordon Brown to turn his moral outrage about vulture funds into action if he becomes Prime Minister and change the law to make the Zambian case the last to appear in a British court.
Meirion Jones produced Greg Palast's Newsnight report on vulture funds.
Newsnight would like to make it clear that DAI and DAI Europe Ltd have absolutely no relationship whatsoever with Debt Advisory International.