The fate of politicians referred to the High Court over the citizenship saga will not be known until at least mid-October.

Key points: Politicians' citizenship cases to be heard in High Court on October 10-12

Politicians' citizenship cases to be heard in High Court on October 10-12 Court to decide fate of Barnaby Joyce, Matt Canavan, Malcolm Roberts, Larissa Waters and Scott Ludlam

Court to decide fate of Barnaby Joyce, Matt Canavan, Malcolm Roberts, Larissa Waters and Scott Ludlam Tony Windsor to join citizenship challenge and argue Joyce breached the constitution

The court held its first hearings on the cases in Brisbane on Thursday, and Chief Justice Susan Kiefel has ordered the matter be heard in Canberra on October 10-12.

It is not clear yet how long it could take the court to decide on the case and announce its decision on the five cases currently before it — those of Deputy Prime Minister Barnaby Joyce, former Nationals Minister Matt Canavan, One Nation's Malcolm Roberts and former Greens senators Larissa Waters and Scott Ludlam.

Solicitor-general Stephen Donaghue QC, acting for the Commonwealth, had urged the hearings be scheduled in mid-September to ease any concerns about the validity of decisions made by the 45th Parliament.

In another twist, Mr Joyce's political nemesis, Tony Windsor, has been given permission to join the citizenship challenge in the High Court.

Mr Windsor will argue Mr Joyce has breached the constitution, as he was a dual citizen of New Zealand.

Mr Windsor's lawyers, appearing by videolink from Melbourne, also argued for the right to cross-examine Mr Joyce if they needed it for their case.

Solicitor-general Stephen Donaghue QC, acting for the Commonwealth, urged the court to hear the matters by mid-September.

Chief Justice Kiefel said she understood the "unusual circumstances" of the challenges, and the "high level of urgency", given it would have an impact on the current make-up of the Parliament.

However, she raised concerns whether the matters could be dealt with that quickly, particularly when Deputy Nationals leader Fiona Nash and South Australian senator Nick Xenophon's cases were awaiting formal referral to the court.

Chief Justice Kiefel asked the solicitor-general whether there was a "real practical difficulty in terms of governance" if the court waited until October to hear the cases, to which Mr Donaghue replied there was not.

Lawyers for Senator Canavan also said the Commonwealth had "underestimated the complexity of their case", given the nature of his Italian citizenship.

They also suggested the highly publicised story he had presented about his mother signing him up for Italian citizenship was "irrelevant", rather arguing that there had been retrospective changes to Italian laws that had led to the strife.

Mr Donaghue said the cases of Senator Canavan, Mr Joyce and Ms Waters were different to those of Senator Roberts and Mr Ludlam.

He argued Senator Canavan, Mr Joyce and Ms Waters had no knowledge they could be considered dual citizens under foreign law.

The solicitor-general but suggested Senator Roberts and Mr Ludlam knew or should have known.

Lawyers for Senator Roberts criticised the initial timing of the full hearings, suggested by the Commonwealth.

They also took issue with the Attorney-General's offer to get the same British QC enlisted to give expert evidence on other citizenship cases to also draft a report about Senator Roberts' status.

The argument was that they should have the chance to brief the legal expert themselves, and have the opportunity to find their own experts if they did not agree.