Labor did not run a candidate in either seat.

After weeks of instability and a leadership change that took place just four days before the poll, the Liberals were bracing for the worst.

Mr Abbott began the day in the electorate saying he was expecting a swing against his party.

"Byelections are traditionally difficult for the incumbent party [and] there is usually a slight swing against the incumbent party," Mr Abbott said.

"I think we can say pretty much for certain that there should be a swing to the Greens, but no one should read into that because they are probably the main opposition here today."

Former Optus executive Paul Fletcher in Bradfield, and one-time Peter Costello staffer Kelly O'Dwyer in Higgins, had both spent weeks trying to convince voters they were supportive of strong action on climate change, including an emissions trading system. But they were forced to spend the last week of the campaign explaining Mr Abbott's decision to oppose the scheme to voters.

The Greens' candidates in both seats quickly capitalised on the Opposition's internal shenanigans, trying to make the byelections about global warming.

Susie Gemmell, the Greens candidate in Bradfield, said voters were telling her they disagreed with Mr Abbott's views on climate change.

"It's an extraordinary turn of events, but the Greens are giving a contest to the Liberal Party on the issue of climate change in their heartland," Ms Gemmell said.

Of the two seats, Bradfield was expected to deliver a more comfortable win to the Liberal Party.

The previous MP, Brendan Nelson, held it with a margin of 13 per cent.