Australia's richest citizen Gina Rinehart is set to keep the rest of her long-running family dispute private, after a High Court ruling in Canberra today.

Key points: Two of Gina Rinehart's children say they want the case heard in public

Two of Gina Rinehart's children say they want the case heard in public They accuse Mrs Rinehart of diminishing assets of trusts from which they benefit

They accuse Mrs Rinehart of diminishing assets of trusts from which they benefit The pair say they signed an agreement for the dispute to be heard privately under pressure

Mrs Rinehart's children, John Hancock and Bianca Rinehart, have accused their mother of unconscionable conduct in the management of trusts from which they benefit.

They allege that she diminished assets of the trusts.

That matter is currently before the Federal Court, and no defence or findings have been delivered in that case.

But Mr Hancock and Ms Rinehart asked the High Court to allow them to challenge the validity of agreements they signed, to fight any disputes over the trusts in confidential arbitration.

The pair said they had signed under pressure and wanted the dispute to be heard in public.

Today the High Court found it would have been clear when the agreements were signed that any challenge would not be determined in the public spotlight.

The court said that was because the agreements were drawn up after Mr Hancock made threats to take legal action.

The case also involved more than 10 other companies and individuals caught up in the dispute between Mr Hancock and Ms Rinehart.

The High Court has also ordered the pair to pay costs.

In a separate case in 2015, Bianca Rinehart wrested control of the family's valuable Hope Margaret Hancock Trust after a battle in the New South Wales Supreme Court.