The US Supreme Court has agreed to rule on whether Argentina's assets are protected from hedge funds seeking to repayment.
In 2002, Argentina defaulted on some $US100 billion worth of debts and has since restructured its debt twice, cancelling around 75% of the nominal value of the bonds.
About 92% of the country's bondholders agreed to write off most of the amount owed to them.
But NML Capital and Aurelius are demanding 100% repayment of $US1.3 billion, plus interest.
Argentina refuses to pay anything to investors who declined to participate in a previous debt reduction deals involving most of the nation's lenders.
The BBC reports investors last year went to court to have an Argentine Navy ship, the Libertad, impounded in Ghana. After several weeks, the ship returned home.
Numerous US courts have said that Argentina must repay the money - most recently in August 2013.
But an appeals court held off forcing Argentina to pay, pending an appeal to the Supreme Court, which is considered unlikely to hear the full case.
In this instance, the BBC says Supreme Court will decide whether the US Foreign Sovereign Immunities Act protects Argentina's property from being seized.
The US Justice Department is taking the side of Argentina. It has urged the Supreme Court to hear the case and strike it down.