South Carolina Governer Nikki Haley and billionaire philanthropist Betsy DeVos are former critics of the Republican
Both women are former critics of Trump. Haley once said she was "not a fan" and DeVos referred to him as an "interloper".
The choice of Haley as UN ambassador has been met with a sense of relief in some circles, according to BBC UN correspondent Nick Bryant.
Senior diplomats had "expected president-elect Trump to downgrade the job of UN ambassador so that it was no longer a cabinet-level position", he says, but Trump's choice of a "political heavyweight" for the role is seen as an "early indication than the incoming administration will take the UN more seriously".
However, Trump's decision to appoint DeVos as education secretary is "already drawing fire from both sides of the political spectrum", says CNN.
The National Education Association, the largest teachers' union in the US, "slammed DeVos within an hour of the announcement for her advocacy of charter schools", which operate with freedom from a number of regulations imposed upon district schools. Conservatives pointed out that she was a supporter of a package of education standards known as Common Core, which Trump opposed.
Trump still has several key cabinet positions to fill, and is expected to announce tomorrow former presidential hopeful Ben Carson as secretary of housing and urban development and General James N Mattis as defence secretary.
According to the New York Times, the Trump transition team remains divided on who to pick for secretary of state. Rudi Giuliani and Mitt Romney are believed to be the two candidates.Trump makes first White House appointments - who's next?
US president-elect Donald Trump has named two key lieutenants as he prepares to take office, installing Reince Priebus, Republican National Committee chairman, as his chief of staff and Stephen Bannon, the former head of Breitbart News, as his chief strategist.
Trump described the two men as "highly qualified leaders who worked well together on our campaign and led us to a historic victory".
The announcement suggests the businessman is hedging his bets, trying to mend his relationship with the Republican Party leadership while retaining the loyalty of the voters who elected him.
Priebus is "a reassuring presence to establishment Republicans", says CNN, and his appointment signals that "Trump may look to build bridges in Washington and keep continuity with longtime Republican agendas, as opposed to make waves from the beginning".
However, Bannon's appointment has "drawn a sharp rebuke from political strategists", says the Washington Post. They see him as "a controversial figure too closely associated with the 'alt-right' movement, which white nationalists have embraced".
Having establishment operative Priebus and anti-establishment Bannon working together will create some "interesting tension", says BBC Washington correspondent Anthony Zurcher. "If correctly harnessed, the energy could provide drive to the nascent Trump administration. If things go wrong, it could tear the place apart," he says.
So who else in the running for the top jobs in the Trump administration?Newt Gingrich
A long-time advocate of Trump, Newt Gingrich is reportedly in line to be the next secretary of state. The 73-year-old political consultant has a long history in the Republican Party, including masterminding the surprise 1994 election victory that wrested control of the House of Representatives from the Democrats.
But he has also been at the centre of a number of controversies, including becoming the first House speaker to be reprimanded for ethical wrongdoing in the 1990s.
"More than anyone else in the modern history of Congress, it's Gingrich who observers credit for bringing the hyperpartisan, obstructionist approach to Washington that we associate with the capital to this day," says Politico.
One former Gingrich staffer told the website: "Donald Trump is making Newt look like a fairly conventional politician. Nobody would have said that back in the day."Rudy Giuliani
Rudy Giuliani, the former mayor of New York, appears to be the frontrunner for the post of the US's top prosecutor, attorney general.
During 9/11, Giuliani became the face of the city's resilience and gained numerous plaudits from across the political spectrum. He was not always well received, though, and was criticised for introducing the controversial "stop and frisk" policy, which opponents claimed was a form of racial profiling.
However, his tenure in New York has been repeatedly praised by Trump on the campaign trail, with the former mayor "making a series of ill-advised remarks but impressing the incoming president with his loyalty", says the Daily Telegraph.
As for what he would do in the role, it appears Trump's election rival Hillary Clinton may not be "locked up", as the president-elect previously claimed.
I just asked Rudy if he would prosecute Clinton as Trump AG: "I have no comment on what I'm going to do and I would never comment on a case"
— Gabriel Sherman (@gabrielsherman) November 9, 2016
Rudy just said "maybe the Clinton chapter is over"
— Gabriel Sherman (@gabrielsherman) November 9, 2016Sarah Palin
Sarah Palin is perhaps the most surprising name on the list, but the 2008 Republican vice-president nominee is believed to be in the running for interior secretary.
She has made a number of gaffes in her time, but "when it comes to women to include in his cabinet Trump is coming up relatively empty", says Bustle.
The role of interior secretary is mainly to oversee the Bureau of Land Management, which fits in with the former Alaska governor's political passions. Last year, Palin told CNN she would be "delighted" to serve in a Trump administration and that "her thing" was "those things that God has dumped on this part of the Earth for mankind's use instead of us relying on unkind foreign nations for us to import their resources".
Trump for his part seems keen. He has said there would "certainly" be a role in his cabinet for Palin.
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