The High Court has decided the so-called internet twins will remain in care as wards of court.
The Birmingham court has ruled that the twins, who have been in care since Thursday, will not return to Alan and Judith Kilshaw.
Flintshire Social Services made the application to have the girls made wards of courts but this ruling was challenged by the Kilshaws. They are also expected to challenge the latest decision.
Mr Justice Kirkwood said the court would remain in control of the case and that the twins would remain where they are, pending research into what was best for them.
The judge said the Kilshaws, from Buckley, north Wales, had given the court solemn undertakings not to discuss the case or any of the arrangements for the twins with anyone unconnected with the hearing.
He added that the case involved legal complexities "since it is not just English law that I have to consider, but the position also in one, two or perhaps three states of the United States of America".
He told reporters after this morning's hearing: "I am sure that everybody understands that this court's task is to do its best to find the right solution for the twins. It's their welfare that really matters in all of this".
The Kilshaws adopted Belinda and Kimberley from their American birth-mother after they paid £8,200 to a Californian internet adoption agency.