The preliminary hearing at the Royal Courts of Justice in London was being heard by judge Andrew McFarlane, the president of the family division of the High Court of England and Wales.
The case concerns Dubai's ruler Sheikh Mohammed bin Rashid Al-Maktoum, 70, and one of his wives Princess Haya, 45, a daughter of the late king Hussein of Jordan and a half-sister of King Abdullah II of Jordan.
After a previous hearing held in private in London, the couple issued a statement relating to the nature of the case.
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"These proceedings are concerned with the welfare of the two children of their marriage and do not concern divorce or finances," it said.
It said the case management hearing would "deal with issues relating to how to proceed to a final hearing to determine the welfare issues".
The case is subject to reporting restrictions. At the judge's direction on Tuesday, only journalists with certified press credentials through media based within the jurisdiction of England and Wales were allowed to sit in on the proceedings.
The two-day hearing is set to continue on Wednesday. Haya arrived at the court accompanied by her lawyer Fiona Shackleton, who represented Prince Charles, the heir to the British throne, in his divorce from Diana, princess of Wales.
Sheikh Mohammed is being represented by Helen Ward, who acted for Guy Ritchie in his divorce from pop star Madonna and for former Formula One motor racing supremo Bernie Ecclestone in his divorce.
A small anti-Sheikh Mohammed demonstration took place outside the courts complex
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