(CNN) Donald Trump holds double-digit leads over Ben Carson in both South Carolina and Nevada, the third and fourth states scheduled to hold nominating contests in next year's race for the presidency, with Trump widely seen in each state as the best candidate to handle a range of top issues, according to new CNN/ORC polls .

Trump holds 38% support in Nevada, with Carson in second with 22%, and in South Carolina, Trump doubles Carson's support, 36% to 18%. No other candidate comes close to those top two in either state; the third-place candidate in each case has less than 10% support.

Trump's backing in both states outpaces his support in most recent national polling, where he tends to draw around a quarter of Republican voters.

In Nevada, where more than half of likely caucus participants say they have made up their mind or are leaning toward someone, Carly Fiorina takes third place with 8%, followed by Florida Sen. Marco Rubio with 7% and former Florida Gov. Jeb Bush with 6%. Texas Sen. Ted Cruz and former Arkansas Gov. Mike Huckabee are next at 4% each, with the remainder of the field at 2% or less.

Trump's supporters in Nevada are more committed than others: Among those likely caucus-goers who say they have made up their minds or are leaning toward someone, 53% support Trump, 21% Carson, 7% Rubio and everyone else is at 5% or less. Those who say they are still trying to decide whom to support break 21% each for Carson and Trump, 12% for Fiorina, 10% for Bush, 9% for Huckabee and 6% for Rubio.

Among all likely voters in South Carolina, Rubio takes third with 9%, followed by Fiorina at 7%, Bush at 6%, Cruz at 5% and the state's senior senator, Lindsey Graham, also at 5%. Kentucky Sen. Rand Paul follows at 4%, with Huckabee at 3% and the rest at 2% or less.

Fewer South Carolina Republican voters say they have made up their minds about whom to support than among Nevada Republicans: 60% say they are still trying to decide, and the difference in candidate support between the two groups is not large enough to be significant.

Trump's lead rests on widespread perceptions that he's the best candidate to handle the economy (67% say so in Nevada, 59% in South Carolina, while no other candidate hits double-digits) and illegal immigration (55% in Nevada and 51% in South Carolina, topping the other candidates by 40 points or more). About 6 in 10 in each state say Trump is the candidate most likely to change the way things work in Washington (60% in Nevada, 58% in South Carolina). Furthermore, nearly half -- 47% in Nevada and 44% in South Carolina -- view Trump as the candidate with the best chance of winning the general election next November.

Trump's strength fades somewhat on foreign policy, handling ISIS and social issues. Although Trump tops all other candidates by significant margins when voters and caucus-goers are asked which candidate would best handle foreign policy (he's up 21 points in Nevada, and 13 points in South Carolina) and ISIS (he tops Rubio by 33 points in Nevada and tops Graham by 27 points in South Carolina), his advantages are smaller than those he's built on the economy and immigration.

Trump is also slightly less dominant on which candidate best represents the values of Republicans like themselves. In Nevada, 34% say that's Trump, 19% Carson, 10% Cruz, 9% Rubio and 7% each Bush and Fiorina. In South Carolina, 25% say it's Trump, 19% Carson, 10% Bush, 8% Rubio, 7% Graham, 6% Cruz, and 5% each Fiorina and Huckabee.

On social issues, Trump runs about even with Carson as most trusted in both states, 25% Trump to 23% Carson in Nevada and 26% Carson to 22% Trump in South Carolina.

Among white evangelical protestants in South Carolina, who made up about two-thirds of South Carolina Republican voters in the 2012 GOP primary and are far more likely than other Republicans to call social issues their top concern (15% among white evangelicals vs. 1% among all other likely GOP voters), Trump tops Carson by 8 points, 32% to 24%, with Rubio at 11%.

In both states, the economy was the top issue for those who say they're likely to participate in the nominating contests, with 39% of Nevada Republicans and 41% of South Carolina Republicans calling it the most important issue in deciding their presidential vote.

The CNN/ORC polls were conducted by telephone October 3-10. A total of 1,009 South Carolina adults were interviewed, including 521 who said they were likely to vote in the Republican presidential primary. In Nevada, interviews were conducted with 1,011 adults, including 285 who said they were likely to participate in the Republican presidential caucus. Results among likely Republican voters in South Carolina have a margin of sampling error of plus or minus 4.5 percentage points; for Nevada Republican caucus-goers, it is 6 points.