A jury which convicted Gerry Adams's brother of sex offences against his daughter was not "properly directed" by the trial judge, a barrister told an appeal court.
Liam Adams, 59, from west Belfast, was found guilty in 2013 of a string of attacks on Aine Dahlstrom when she was aged between four and nine in the late 1970s and early 1980s.
He was subsequently handed a 16-year sentence, only half of which he is expected to spend behind bars.
His case is being heard in the Appeal Court in Belfast where the defence said part of the judge's charging of the jury may have put the burden of proof on Adams.
Defence barrister Eilis McDermott said: "It comes nowhere near the careful direction that a judge ought to give the jury in a case of this kind."
Adams, formerly of Bernagh Drive, was found guilty of 10 offences against Mrs Dahlstrom - three counts of rape, four of indecent assault and three of gross indecency.
Ms McDermott said part of Judge Corinne Philpott QC's summing up to the jury had been "opaque" and difficult to follow.
"The consequence of it feeds into the criticism that is made of the learned judge, that the jury was not properly directed. This was an issue of credibility."
She cited a "wholly inflammatory direction about consent and recklessness" when there clearly was no consent by a child of Ms Dahlstrom's age.
One of the judges hearing the appeal, Lord Justice John Gillen, said he could not recall a case where no reference was made by the trial judge to the defence evidence.
"Is it not unconventional? There is no reference to his evidence at all that I can find and there is no reference to his witnesses."
The opportunist predator committed the crimes when he was left alone with his daughter, often sneaking into her room while she slept.
The abuse was committed over a five-year period between 1977 and 1981. In later years he went on to work in a number of youth centres in Northern Ireland and the Republic of Ireland.
Mrs Dahlstrom, now in her early 40s, has waived her right to anonymity.
The conviction heaped pressure on Gerry Adams to explain why he did not alert the authorities to the abuse allegations when he initially learned of them.
The Sinn Fein leader has insisted he acted properly and accused political rivals of exploiting a family issue to attack him.
A document had been discovered by Gerry Adams' former solicitor which should have been disclosed during Adams' trial, Ms McDermott said.
She added: "It certainly was material that would have been used in cross-examination."
Liam Adams wore a red checked shirt and listened intently to the deliberations. His wife Bronagh and daughter Claire Smith sat in the public gallery.
Ms Dahlstrom first complained to police in 1986 but subsequently withdrew the allegation, the court was told. She approached police a decade later and reinstated her complaint.
Adams was interviewed by detectives in February 2007 and left the jurisdiction for the Republic of Ireland.
He later handed himself in to police on Sligo and was extradited to Northern Ireland under a European Arrest Warrant.
His first trial collapsed in 2013 and he was tried and convicted in the autumn of that year.
A panel of senior judges, Lord Chief Justice Sir Declan Morgan, Lord Justice Gillen and Lord Justice Patrick Coghlin, heard the appeal.
Ms McDermott said publicity surrounding the trials and particularly Gerry Adams' evidence had made it a national issue throughout Ireland.
She noted the trial judge had omitted to tell the jury that Liam Adams did not have to prove anything. The main thrust of her complaint surrounded Judge Philpott telling the jury that a defendant's evidence must be viewed with the same standard as that of a prosecution witness.
Ms McDermott characterised that as the judge telling jurors the defendant did not have to prove his innocence, but following it with a but.
It is at the very least open to the danger that the jury may have thought that in this case because the defendant did give evidence that in some way the burden of proof reverted to him.
"There is a major cause for concern in relation to the clarity of the direction that has been given to the jury on this fundamental point."
Prosecution barrister Ciaran Murphy QC said it was a case where the judge was not required to review any piece of evidence.
"There was no evidence other than the complainant. The jury were very much focused upon deciding whether they believed Aine Adams or whether they accepted the evidence of the defendant."
The appeal judges challenged him about why two other children of Adams said they had a happy upbringing yet Judge Philpott did not mention it.
Mr Murphy said: "It was close in the minds of the jury towards the end of the trial. It is not something that could have been forgotten by the jury - that Mr Adams put his children into the witness box."