Italy's top court is to decide whether to uphold the convictions of American Amanda Knox and Italian Raffaele Sollecito for the 2007 murder of British student Meredith Kercher.
The former lovers were convicted for the second time last year.
The Court of Cassation must now choose whether to confirm the conviction or order a retrial.
Knox and Sollecito have maintained their innocence throughout and have already served four years in prison.
Leeds University student Meredith Kercher, 21, from Coulsdon, south London, was found dead in the flat she shared with Knox, now 27, in Perugia, central Italy, where both women were studying.
Her partially-clothed body was found under a duvet in her bedroom, which had been locked from the inside. Her throat had been cut.
Prosecutors claimed she was killed as part of a bungled sex game and Knox and Sollecito, 30, were convicted of the murder by a trial court in Perugia in 2009.
They were freed in 2011 after an appellate court overturned the convictions.
The Court of Cessation rebuked the the appellate judge's reasoning and last year an appeals court in Florence sentenced Knox to 28 years and Sollecito to 25 years.
Sollecito, from Bari, southern Italy, has remained in the country, but a definitive conviction would trigger attempts to extradite Knox who lives in Seattle in the US.
Rudy Hermann Guede, born in the Ivory Coast, who opted for a fast-track trial, is serving a 16-year sentence for his role in the murder.
The high-profile case has inspired books and at least two films, and Kercher's family has said Meredith, the real victim, risked being forgotten.
Originally portrayed as a fast-living partygoer, Knox came to be seen in much of her home country as a victim of a botched investigation and an unwieldy justice system.
The US state department has said officials are monitoring the case.
