A judge is to hear a custody application by the natural father of the internet twins, Belinda and Kimberley.
Aaron Wecker is expected to have his case heard in St Louis, Missouri.
Judith and Alan Kilshaw adopted the twins last month from a California-based internet baby broker.
The Kilshaws, from Buckley, north Wales, acquired the girls in Arkansas before bringing them to Britian.
Californian couple Richard and Vickie Allen claim the babies were sold to them before they were tricked into returning them to their natural mother, Tranda Wecker.
Flintshire social services took the twins from the Kilshaws on the eve of January 18.
The babies were made the subject of an emergency protection order pending Flintshire's application for the High Court to make them wards of court.
The High Court proceedings have been adjourned until next month.