Court of Appeal judges will decide whether doctors should keep providing life-supporting treatment to a brain-damaged baby boy today.
Four-month-old Midrar Ali, from Manchester, was declared brain dead by a high court judge last month, but his parents are challenging the decision that his law support could lawfully end.
Last week the case was adjourned after the family were granted legal aid, meaning that they could appoint a new legal expert.
The Court of Appeal judges agreed to adjourn the case until today, for a hearing in London, to allow Lord Brennan QC more time to prepare for the case.
Midrar was starved of oxygen due to complications at birth and had been placed on a ventilator at St Mary's Hospital in Manchester.
The hospital's legal team applied to the courts for ventilation to be lawfully withdrawn, allowing Midrar a "kind and dignified death".
Lawyers representing Manchester University NHS Foundation Trust said experts have confirmed brain stem death.
Neil Davy, representing the trust, opposed the adjournment, saying: "We do say it would be undignified and unkind to delay matters unnecessarily."
He said the parents' case had properly been presented at the High Court at the previous hearing.