Published Tuesday, 27 November 2012
Tweed, who played for Ireland and Ulster, was accused of abusing two young girls who are now adults over an eight-year period.
The Ballymena councillor has denied all 14 counts of indecent assault, gross indecency and inciting gross indecency during his three-week trial at Antrim Crown Court.
Jurors began their deliberations at 10am on Tuesday but at 3.20pm the 10 women and two men said they could not reach unanimous verdicts.
Judge Alistair Devlin then said he would accept majority verdicts so at 4pm the jurors returned to court number two.
One of Tweed's alleged victims wept in the courtroom while the 53-year-old accused, of Clonavon Terrace in Ballymena, stood impassively in the dock.
The jury foreman said they were unable to reach majority verdicts on 13 of the counts but found David Tweed not guilty of one of the indecent assault charges.
He has now been remanded on continuing bail and the jury will return on Wednesday morning to consider the remaining charges.
David Alexander Tweed was capped five times for Ireland and played in the 1995 Rugby World Cup in South Africa.
He also played more than 30 times for Ulster during the 1980s and 1990s.
Tweed's defence barrister said he had been the victim of a spiteful conspiracy and claimed the girls' memories had become distorted with the passage of time.
Meanwhile the prosecution accused Tweed of using his sporting achievements and position in society to live a lie, adding the claimants had no reason to make up the allegations.
Judge Devlin told the jurors they must put aside any prejudice they may have towards those accused of sex abuse as well as any sympathy for people who claim to be victims.
He added: "You must approach the issue of a true verdict with an open mind."
© UTV News