The hearing will resume into the case of terminally-ill baby Charlie Gard.
It is the latest round of a legal battle mounted by his parents, Chris Gard and Connie Yates, who want him to undergo a therapy trial in the United States.
The 11-month-old suffers from a rare genetic condition and has brain damage.
Specialists at Great Ormond Street Hospital in London, where Charlie is being cared for, say the therapy will not help and life-support treatment should stop.
The couple, who are in their 30s and come from Bedfont, west London, have already lost battles in the High Court, Court of Appeal and Supreme Court in London.
They have also failed to persuade European Court of Human Rights judges to intervene.
In April, a judge ruled in favour of Great Ormond Street and said Charlie should be allowed to die with dignity.
The hearing is due before Mr Justice Francis in the Family Division of the High Court in London on Friday.