The six are members of two Syrian families who fled their war-torn native land and arrived in Greece where they sought asylum.
They claim their rights have been breached by an EU-Turkey arrangement providing for the return of new irregular migrants arriving in Turkey since March 20. Their case is against the EU, European Council, and Irish State.
Since the case began, one of the families, a man and his teenage daughter, have received a positive decision in relation to an application to be transferred to Germany to be reunited with other members of the family, the court heard.
The other family, a couple and their two daughters, is also seeking a transfer to Germany where they also have family.
The defendants deny the claims.
Yesterday, Mr Justice Tony O’Connor began hearing applications by the EU and State parties seeking the dismissal of the case over lack of jurisdiction.
Maurice Collins, for the EU parties, said the families have no connection whatsoever with this State, any agency of the State, or any public authority here. With the exception of their lawyers, there appeared to be no connection with any citizen of this State.
The case continues.