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The firms, described as "vulture funds" by critics, are suing for more than $20m (ÂŁ12m) - some 5% of the Liberian government's total budget this year.
Liberia says it has no money to pay the debt back and has accused the firms of profiting from poverty.
The country is recovering from a 14-year civil war which ended in 2003.
The details of the case are still unclear, but it is thought that Liberia borrowed $6.5m from the US-based Chemical Bank in 1978 and that debt may have been resold a number of times.
The two funds are requesting that London's High Court grant a summary judgement in the case - making Liberia liable for the debt without the need for a full hearing.
'Tooth and nail' fight
In 2002 a New York court ruled that Liberia owed $18m - the current case is an attempt to collect that sum plus interest.
At the time of the New York case Liberia was wracked by civil war and did not offer a defence.
Liberian Finance Minister Augustine Kpehe Ngafuan told the BBC's Network Africa programme the country could not afford to repay the debt.
"We're asking everybody, we are asking even the court not to grant them summary judgement. Let them go through the normal procedure," he said.
"Our lawyers are going to work tooth and nail to battle this."
He said he hoped that the international community would take action to make sure that "these people that survive on poverty do not thrive".
UK activists are lobbying the government to change the law so such cases cannot be heard in UK courts.
Nick Dearden, of Jubilee Debt Campaign, said: "This case is absolute proof that you can't tackle vultures by voluntary means.
"Currently these companies don't have to tell us anything about themselves because they're registered in tax havens - they can just turn up in London and sue one of the poorest countries in the world."
Very little is known about the funds - Hamsah Investments and Wall Capital.
Hamsah was awarded more than $11m in a similar action against another poor country, Nicaragua.
The BBC's economics correspondent Andrew Walker says vulture funds are controversial - especially when they target nations already receiving debt relief on what they owe to rich countries.
Sometimes that debt relief is what frees the resources to pay creditors who take legal action, our correspondent says.
The solicitor representing Hamsah has not yet responded to requests for comments on the case.
Source: BBC
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