Judges in the European Court of Human Rights are starting to analyse the case of a terminally-ill baby who has been at the centre of a high-profile legal battle in London.
Chris Gard and Connie Yates want 10-month-old Charlie Gard, who suffers from a rare genetic condition and has brain damage, to undergo a therapy trial in the US.
Specialists at Great Ormond Street Hospital for Children in London, where Charlie is being cared for, say therapy proposed by a doctor in the US is experimental and will not help.
They say life support treatment should stop.
Charlie's parents hope that judges in the European Court of Human Rights, in Strasbourg, France, will come to their aid after losing battles in the High Court, Court of Appeal and Supreme Court in London.
Their lawyers on Monday filed detailed legal arguments and Strasbourg judges say they will treat Charlie's case with the "utmost urgency".
Supreme Court justices in London have said Great Ormond Street specialists should keep providing life-support treatment until midnight on July 10 to give European court judges time to consider the case.
A European Court of Human Rights spokeswoman says the case will get "priority".
Charlie's parents have exhausted legal options in the UK.
A High Court judge in April ruled against a trip to America and in favour of Great Ormond Street doctors.
Mr Justice Francis concluded that life-support treatment should end and said Charlie should be allowed to die with dignity.
Three Court of Appeal judges upheld that ruling and three Supreme Court justices dismissed a further challenge by the couple.
Mr Justice Francis made a ruling after a trial in the Family Division of the High Court in London.
He heard that Charlie, who was born on August 4 last year, has a form of mitochondrial disease, a condition which causes progressive muscle weakness and brain damage.
Specialists in the US have offered a therapy called nucleoside.
During hearings in London, barrister Richard Gordon QC, who leads Charlie's parents' legal team, has given indications of the case the couple are mounting in the European court.
He has suggested that British government ministers may be in breach of human rights obligations as a result of decisions by judges in London.
He has said parents should be free to make decisions about their children's treatment unless any proposal poses a risk of significant harm, and suggested that Charlie's rights to life and liberty might have been breached and the couple's right to respect for family life infringed.