Libya's Supreme Court says it will rule on 11 July on the final appeal of six foreign medical workers condemned for infecting 438 children with HIV.
Libya's highest court could commute the death sentences
Five Bulgarian nurses and a Palestinian doctor say they are innocent of giving tainted blood to the children.
The court is expected to uphold their death sentences but may leave a final decision to the High Judicial Council.
The sentences may be commuted in exchange for a compensation package for the children's families.
Fifty-six of the 438 children infected with tainted blood at the Benghazi hospital in 1998 have since died.
Outside the Tripoli courtroom, relatives of the affected children gathered, with many parents holding images of their sons and daughters.
A Libyan spokesman for the victims' families, Ramadan al-Fitouri, told the BBC he was certain the court would uphold the death sentences.
"I am confident that the Supreme Court will have no option but to uphold the sentence... I think the court will issue its ruling... within 10 to 15 days," he said.
The medics have argued that poor hygiene was to blame for the infections.
During their trial, one of the doctors who helped first isolate the HIV virus, Luc Montagnier, testified that the hospital epidemic began before the accused started working at the hospital.
But the six were found guilty and sentenced to death twice, first in 2004 and again in 2006 following a court appeal.
This hearing will be their final appeal in a case which has gripped public attention in both Libya and Bulgaria.
The European Union and the US have both been involved in the talks over a possible deal.
During a visit to Bulgaria last week, US President George W Bush appealed for the release of the medics.
On Tuesday, Bulgaria announced that it had granted citizenship to the Palestinian doctor, ensuring that he would be part of any deal reached after the verdict.