The King of Jordan had taken a personal interest in the case, a representative of the Jordanian embassy in London said during the proceedings in Coleraine, Co Londonderry.
The two wheelchair-bound power lifters and a trainer were arrested on Monday evening and accused of sexual offences involving two women and two underage girls, the court heard.
Weightlifter Omar Sami Qaradhi was charged with three counts of sexual assault and one of voyeurism on Wednesday. Two of the alleged assaults were against children.
His colleague Motaz Al-Junad faced one sexual assault charge. Trainer Faisal Hammash was charged with two counts of causing a child to engage in sexual acts.
The 19-strong Jordanian squad was one of several from the Middle East and Africa training in Northern Ireland's Antrim Forum sports centre ahead of the London games, which are due to start on Aug. 29.
The team was due to leave for London on Wednesday but it was not clear whether the three accused would join them.
The court was told the alleged offences had taken place between August 16 and 20.
A representative of the Jordanian embassy from London said in court her country would provide guarantees the men would return to face trial if granted bail.
