The Caribbean's final appeals court is being asked to overturn a key ruling by the UK's Privy Council and allow the death penalty to be carried out.
The Barbados authorities want to hang two men convicted of murder in 1999.
They are asking the Caribbean Court of Justice (CCJ) to overrule the Privy Council's decision that execution must happen within five years of conviction.
The CCJ was set up last year, replacing the Privy Council as the appeal court for most of nations in the Caribbean.
The hearing, which began on Tuesday, is being described as the first real test of the Trinidad-based CCJ.
The Barbados government wants to be allowed to hang two men, Lennox Boyce and Jeffrey Joseph, who were convicted of beating another man, 22-year-old Marquelle Hippolyte, to death in 1999.
However, a landmark ruling by the Privy Council in London in 1993 stated that keeping someone on death row for more than five years was cruel and inhumane.
Since then, defence lawyers have often managed to get death sentences reduced to life in prison by pursuing an appeals process that goes beyond the five-year limit.
Crime rates
Lawyers for the Barbadian government are expected to argue that the time restriction is an arbitrary limit.
Many Caribbean countries see the death penalty as a way to tackle surging crime rates.
However, legal experts do not expect the new court to set a new precedent.
"This is their first death penalty case," Gregory Delzin, a leading anti-death penalty lawyer, told the Associated Press news agency.
"They're not going to come out of the barn with their guns blazing."
Until last year, final appeals were traditionally referred to the Privy Council in London, made up of senior judicial figures.
The CCJ was designed to replace the Privy Council, seen as a vestige of British colonial power in the Caribbean.
However, only Barbados and Guyana have so far passed legislation to accept the CCJ's jurisdiction.
Other countries which signed up to the CCJ are still in the process of passing the required laws.
Many of the countries in the Caribbean retain hanging as a means of execution.
The last execution in the region was in the Bahamas in 2000.
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