The parents of a 12-year-old boy at the centre of a life-support dispute say their wishes and beliefs have not been given "proper weight", a court heard.
Archie Battersbee was found unconscious at home in Southend, Essex, on 7 April and doctors believe he is brain dead.
Last week a second High Court judge ruled it was in Archie's best interests to have hospital treatment withdrawn.
The latest Court of Appeal hearing challenging that decision began on Thursday.
Archie has not regained consciousness since his mother found him. She believes he had taken part in an online challenge.
Doctors treating Archie at the Royal London Hospital in east London said tests showed he was "brain-stem dead" and argued continued life-support treatment was not in his best interests.
Archie's parents have disagreed and said his heart was still beating.
Lawyers for the boy's parents, Hollie Dance and Paul Battersbee, told Court of Appeal judges that Mr Justice Hayden, who oversaw the second High Court hearing, had not given "real or proper weight" to Archie's previously expressed wishes and religious beliefs.
Edward Devereux QC also argued the judge failed to carry out a "comprehensive evaluation" of the benefits and burdens of continuing life-support treatment, and had been wrong to conclude that treatment was burdensome and futile.
High Court judge Mrs Justice Arbuthnot initially considered the case in June and concluded Archie had already died. The case went back to the High Court for a second time following an appeal.
Sir Andrew McFarlane, president of the Family Division of the High Court and the most senior family court judge in England and Wales, Lady Justice King and Lord Justice Peter Jackson began considering arguments on Thursday.
The hearing is due to resume on Friday.
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