Nick Xenophon Team's Rebekha Sharkie has won the South Australian seat of Mayo, while the party has declared it is hopeful of further wins in coming days.

Ms Sharkie took Mayo from former Liberal frontbencher Jamie Briggs — with more than 74.7 per cent of the vote counted she had 55.7 per cent of the vote.

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Ms Sharkie said she owed "immense gratitude to the people of Mayo for taking a chance on me for the first time".

She said, while campaigning, people were not talking about a late-night incident involving Mr Briggs and a female public servant in Hong Kong.

Ms Sharkie said people were focused on health, youth unemployment and road infrastructure.

Earlier in the night she said she felt "so privileged".

"You have to dream big, so I've been dreaming big for a while and just working really, really hard," she said.

Mr Briggs has tweeted a concession.

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The seat of Mayo was considered a very safe Liberal seat.

Mr Xenophon described the win as historic and said it showed that voters felt neglected by the major parties.

In his speech thanking candidates, volunteers and supporters, the party's leader declared "we have broken the duopoly, we're gonna build from that".

NXT tipped to win three Senate seats

He said it was likely the party would have three senators in Parliament, with the number two spot going to Stirling Griff, who has been a long-time backroom supporter of Senator Xenophon.

The third senate position candidate Skye Kakoschke-Moore has worked in Senator Xenophon's office for the past six years.

There is also a chance NXT could pick up a second House of Representatives seat with a win in South Australia's massive country electorate of Grey where Port Lincoln's Andrea Broadfoot is a whisker away from defeating sitting Liberal MP Rowan Ramsey.

"Here is an opportunity to do something great for our state, to do something great for our country," Mr Xenophon said.

"There is real space for the political centre in this country, millions of Australians feel left out by the major parties and we're here to fill that void once and for all."

After the speech by Senator Xenophon and Ms Sharkie to the party's faithful in Adelaide, Mr Griff told reporters he believed NXT was in the running to pick up one or two Senate seats in other states.

"We will easily have four which is four times the firepower for South Australia."

Queensland and Victoria are the most likely states to elicit a quota for another NXT candidate, although that was looking increasingly unlikely.

Senator Xenophon was all smiles but there's a chance he will have to concede a potentially costly loss. In the dying days of the campaign he promised local journalists he would hand over bottles of the well known, and expensive, South Australian Grange wine if the result was a hung parliament.

Senate result to take days

Liberal Education Minister Simon Birmingham said the outcome of the Senate vote may not be known for days.

Senator Birmingham said he expected NXT to secure at least three Senate seats.

"I would assume, based on the strength of his Lower House vote, that Nick will get at least three senators," he said.

"He could do a little better than that, but that really is completely up in the air and I wouldn't want to speculate beyond that."

ABC commentator Antony Green said it appeared from early counting the NXT had "not polled as well as expected" in the House of Representatives with a little over 20 per cent.

He said there were no Senate figures yet and it would be interesting to see the differences in voting between the houses.

NXT a phenomenon: Bishop

Senior Liberal Scott Morrison said he felt strongly for Mr Briggs.

"Jamie is a guy with a lot of talent, ability and I doubt that's the last we've seen of Jamie Briggs in politics I would hope," he said.

"I wish him and everyone all the best."

Senior Liberal Minister Julie Bishop described the NXT as a "phenomenon".

"People are turning to it," Ms Bishop said.

"I seriously don't understand it, because Nick, himself, can't deliver anything.

"He can't deliver a budget. He can't deliver debt relief.

"He can't provide any policies that would be implemented.

"So I guess it's a protest vote."

Meanwhile, Christopher Pyne has declared victory in the seat of Sturt, with the Liberals also holding on to Barker and Boothby.

In Hindmarsh, Labor's Steve Georganas is hopeful of a win against the Liberals' Matt Williams.

Labor has retained Kingston, Port Adelaide and Wakefield, and is also expected to hold on to Kate Ellis' seat of Adelaide.