The Cook Islands Appeal Court is hearing a challenge over the win by the caretaker prime minister, Dr Robert Woonton, in his Manihiki electorate.
The court, which is sitting in Auckland, New Zealand, will also be hearing points of law connected to four other electoral outcomes, including that of the former speaker, Sir Pupuke Robati.
The chief registrar, Terry Hagan, says the court will decide on whether there is a conflict between the Electoral Act and the constitution.
And, he says it centres around whether challenges can be made to voters on the grounds of what consituency they vote in.
"I think in simple terms, it means that once the registration is closed and the process of objections has been completed, prior to the election, then that whole matter cannot be revisited after the election."
Mr Hagan says there were originally six petitions but they've received information that one for Penrhyn has been discontinued.