Three Court of Appeal judges are preparing to analyse the case of a sick baby whose parents want him to travel abroad for treatment they hope will save his life.
Chris Gard and Connie Yates want permission to take son Charlie to America for a therapy trial.
Last month a High Court judge ruled that doctors in Britain could stop providing life-support treatment.
Charlie's parents hope that the three appeal judges will overturn Mr Justice Francis's decision.
Lord Justice McFarlane, Lady Justice King and Lord Justice Sales are listed to consider evidence at a Court of Appeal hearing in London on Tuesday.
Mr Justice Francis decided that doctors could stop providing life-support treatment to nine-month-old Charlie on April 11, after analysing the case in a hearing at the Family Division of the High Court in London.
Charlie's parents, who are in their 30s and come from Bedfont, west London, want a specialist in America to provide therapy.
Specialists at Great Ormond Street Hospital, where he is being cared for, disagree and say life-support treatment should stop.
Mr Justice Francis ruled in Great Ormond Street's favour and concluded that Charlie, who suffers from a rare genetic condition and has brain damage, should move to a palliative care regime.
Great Ormond Street bosses said treatment would continue until appeal judges had made decisions.
Mr Justice Francis heard that Charlie, who was born on August 4, had a form of mitochondrial disease, a condition which causes progressive muscle weakness and brain damage.
Specialists in the US had offered a therapy called nucleoside, but the judge said experts agreed that the treatment could not reverse Charlie's structural brain damage.
Charlie's parents had appealed for money on a GoFundMe website to cover doctors' bills in the US and reached their £1.2 million target shortly before the High Court trial.
People have continued to give money despite Mr Justice Francis's decision and the fund has topped £1.3 million.
Mr Justice Francis said Great Ormond Street doctors had considered the experimental treatment, but decided it would not help Charlie.
He said the case had never been ''about money''.