Australians in a suburb of Sydney are voting in a by-election that could cost the governing conservative coalition its slim majority in parliament.
The poll was called after Bennelong MP John Alexander stepped down in a row over dual citizenship.
The citizenship crisis has forced nine Australian MPs to resign.
Mr Alexander, of the Liberal-National coalition, is standing for re-election but faces a strong challenge from Labor's Kristina Keneally.
A loss for Mr Alexander would see Prime Minister Malcolm Turnbull lose his one-seat majority in parliament.
The government would then have to rely on the support of five independents to push through its programme.
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"People will be casting a judgment on the government, which I lead, of course," Mr Turnbull told reporters.
Australia's constitution demands politicians are not dual nationals.
Mr Alexander, a former tennis star, resigned after revealing that he had probably inherited dual British citizenship through a UK-born parent.
He said at the time that he could "no longer... maintain the belief" he only held Australian citizenship. However, it emerged that he might not even be entitled to UK nationality and so he is re-contesting the seat.
Among the politicians unseated by the citizenship crisis was Deputy Prime Minister Barnaby Joyce. Mr Joyce easily won a by-election earlier this month and returned to parliament.
Mr Turnbull has unveiled plans to make all federal politicians clearly declare their citizenship status to avoid a similar crisis in the future.
Under the new plan, politicians will be obliged to make a formal declaration about their citizenship status, as well as provide details about the time and place of their birth, and the time and place of birth of their parents.
If any politicians formerly had citizenship of another country they will also be required to detail when and how they renounced it.