Deputy Prime Minister Barnaby Joyce, Nationals Senators Fiona Nash and Matt Canavan, and South Australian Nick Xenophon will either all survive their citizenship challenges or all be kicked out, according to the Solicitor-General.

They are four of the seven politicians facing a fight for their political lives and reputations, after it was revealed they were dual citizens.

That rules them ineligible to hold office under the Constitution.

Solicitor-General Stephen Donaghue QC appeared before the High Court this morning, and said the facts of law in those four cases were very similar.

He told the court it was "virtually inevitable that they will stand or fall together".

One Nation Senator Malcolm Roberts' tenure in the upper house is also being questioned.

He will be cross-examined as to the exact chain of events that led to his renunciation of his British citizenship next Thursday.

Lawyers for Senator Roberts also disputed the expert evidence of a British barrister Laurie Fransman QC that the Commonwealth had enlisted to provide advice on the One Nation senator's citizenship.

Senator Roberts' lawyers want to present the court with their own evidence to contradict Mr Fransman, provided by a junior barrister in the same London chambers.

Chief Justice Susan Kiefel ordered Senator Roberts' lawyers to ensure both experts had discussed their findings, so any dispute would be quicker to resolve.

She said "seeing as they're in the same chambers, they shouldn't have to walk very far" to compare their reports.

Joyce should have known he was a Kiwi, argues Windsor

Lawyers for former MP Tony Windsor told the court they want to produce expert legal advice on French, German and US citizenship law as part of their challenge to Mr Joyce's eligibility for Parliament.

Mr Joyce comprehensively defeated his political nemesis at last year's federal election.

Mr Windsor's lawyers said the evidence of other countries' citizenship law would assist their argument that being a foreign national by descent is not a new concept, and was well understood around the world at the time Australia's constitution was being drafted in the late 1800s.

Last month, the Solicitor-General had suggested Mr Joyce, Senator Canavan, Senator Nash, and former Greens senator Larissa Waters would not have known they could have been dual citizens.

The full hearings in all seven citizenship cases will be heard on October 10, 11 and 12.