7:36 p.m. Cruz and Rubio are now battling for second place.
7:30 p.m. CBS News now projects that Trump will win South Carolina's GOP primary.
7:29 p.m. CBS News reports Trump has a narrow edge over Cruz and Rubio.
7:19 p.m. More than half of Republican voters, 53 percent, said they feel betrayed by their own party. Forty-four percent said they don't feel betrayed.
7 p.m.Donald Trump, Ted Cruz and and Marco Rubio are locked in a three-way race, far ahead of the rest of the pack, according to CBS News exit polling.
6:09 p.m. Forty-one percent of voters said Trump is running the most unfair campaign while a third said the same of Ted Cruz.
5:58 p.m. More than half of Republicans said they made up their mind about who they were going to support last month, or even before that. On the other hand, 45 percent said they decided in the last week, 24 percent decided in the last few days and 14 percent made their decision today.
5:52 p.m. More than 95 percent of GOP primary voters said they are either somewhat or very concerned about the future of the nation's economy. Two percent said they are not concerned with the economy.
5:44 p.m. More than half of GOP voters, 53 percent, said they support offering illegal immigrants working in the U.S. the chance to apply for legal status. Forty-three percent, meanwhile, said those who are in the U.S. illegally should be deported and sent back to their country of origin.
5:41 p.m. GOP voters in South Carolina are almost evenly split on whether they prefer a candidate from the establishment vs. a political outsider. Forty-eight percent said they prefer that the candidate has experience and 46 percent said they prefer someone from outside the establishment. This closely mirrors what voter in New Hampshire told pollsters.
5:33 p.m. Three-quarters of GOP primary voters support Donald Trump's proposal to block Muslims from entering the United States. Twenty-three percent, on the other hand, said they oppose the proposed ban.
5:27 p.m. More than half of voters said they are dissatisfied with the way the government is working and 40 percent said they are angry. Only 7 percent said they are satisfied with how the federal government is working.
5:23 p.m. More than three quarters of voters in the South Carolina primary say it matters either a great deal or somewhat that a candidate share his religious values. Less than a quarter, by contrast, say it doesn't matter at all.
5:00 p.m. Early exit polling results is beginning to come in from South Carolina's GOP primary soon. The state's Republican voters have been showing up to their polling sites throughout the day to cast ballots in the GOP's third presidential nominating contest.
Early exit polls in South Carolina suggest that voters see terrorism as the most important issue facing the country (32 percent), followed by those who see the economy (28 percent) and government spending (27 percent) as the most critical issues. In contrast only one out of 10 respondents said that immigration is the most important issue facing the nation.
Voters are choosing among Donald Trump, Ted Cruz, Marco Rubio, Jeb Bush, Ben Carson and John Kasich.
Polls are slated to close at 7 p.m. EST. Meanwhile, the results are coming in quickly from Nevada's Democratic caucuses.
Trump has consistently led the GOP pack in South Carolina, though some recent polls have indicated a tightening race. A Wall Street Journal/NBC News/Marist poll released Friday, for example, found he now only leads his closest rival, Cruz, by five percentage points with 28 percent support. A Bloomberg Politics pollreleased Wednesday found Trump with a 19-percentage-point advantage over Cruz. Thirty-six percent said they back Trump and 17 percent support Cruz.
A CBS News national poll released Thursday found Trump with a 17-percentage-point lead over Cruz.
CBS News Poll Analyst Jeanne Zaino contributed to this story.
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