Donald Trump has won the South Carolina primary in the Republican race for president, cementing his status as the man to beat for his party's nomination.
In the Democratic contest, Hillary Clinton beat Vermont Senator Bernie Sanders in a tight race in Nevada.
Both results will be key ahead of the "Super Tuesday" round on 1 March, when a dozen more states make their choice.
Donald Trump has won the South Carolina primary in the Republican race for president
Republican senators Ted Cruz and Marco Rubio are currently locked in a battle for second place in the state.
Donald Trump's supporters erupted in a roar at his campaign headquarters in Spartanburg when the projected results were announced.
The New York billionaire's campaign has been dogged in controversy, with his latest spat with the Pope on Christian values hitting the headlines this week.
"This one is for you," Hillary Clinton told her supporters in a victory speech in Las Vegas
Mr Bush, once considered a frontrunner, has scoffed at the possibility of Mr Trump winning the Republican nomination.
"Trump can't win, plain and simple,'' he told reporters on Saturday, adding: "He can't be president. A ton of people would be very uncomfortable with his divisive language and with his inexperience in so many ways."
Mr Cruz and Mr Trump won the first two states - the Texas conservative firebrand victorious in Iowa and businessman Mr Trump winning in New Hampshire.
Hillary Clinton, who won Iowa but was beaten convincingly in New Hampshire by Mr Sanders, declared victory earlier in Nevada in a tweet saying "this is your win".
"Some may have doubted us, but we never doubted each other," Mrs Clinton told supporters at a victory rally in Las Vegas. "This is your campaign."
The presidential race between Hillary Clinton and Bernie Sanders has grown increasingly close in recent weeks, with the former secretary of state expected to win Nevada in double digits just weeks ago.
But the Vermont senator, who has successfully galvanised young voters with his calls for free university education, appears to have performed better than expected with the heavy minority population in Nevada.
According to NBC exit polls, Mr Sanders won among Hispanics with 53% of the vote but lost among black voters earning just 22% of their vote.
"Five weeks ago we were 25 points behind and we ended up in a very close election. And we probably will leave Nevada with a solid share of the delegates," Bernie Sanders said in a statement on his rival's victory.
The state represents the most racially diverse battleground so far, with both candidates courting the vote of African Americans, Hispanics and Asian Americans, who make up about 50% of the state's population.
Key Points
Donald Trump has swept to victory in South Carolina, sealing his place as the Republican to beat Former Florida Governor Jeb Bush has dropped out of the race Ted Cruz and Marco Rubio are in a tight race for second place Democrat Hillary Clinton earlier won the Nevada caucuses ahead of Bernie Sanders Mrs Clinton declared victory in a tweet, thanking people who voted for her, saying "this is your win" Results will be key ahead of "Super Tuesday" when a dozen states vote on 1 MarchMrs Clinton's next test will be in the Democrats' South Carolina primary on 27 February. Republicans will hold their own caucuses in Nevada on Tuesday.
Once each state has voted in the primaries or caucuses, the delegates won by each party candidate will go on to endorse them at party conventions in July.