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Donald Trump remains ahead in the early Republican nominating contests of Iowa and New Hampshire, but his lead has shrunk from a month ago, according to brand-new NBC News/Wall Street Journal/Marist polls of these two states.

The polls were conducted Sept. 23-30 - so after the second Republican presidential debate, as well as after Scott Walker's withdrawal from the GOP field.

In New Hampshire, Trump now holds a five-point advantage over Carly Fiorina among GOP primary voters, 21 percent to 16 percent - followed by Jeb Bush in third at 11 percent, and Marco Rubio and Ben Carson tied at 10 percent each.

But a month ago, Trump's lead over the nearest competition in the Granite State (John Kasich) was 16 points, 28 percent to 12 percent.

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And in Iowa, Trump is ahead of Carson by five points among potential GOP caucus-goers, 24 percent to 19 percent - with Fiorina in third at 8 percent, Bush at 7 percent, and Ted Cruz, Rubio and Bobby Jindal tied at 6 percent.

A month ago, Trump's lead over Carson in Iowa was seven points in the same poll, 29 percent to 22 percent.

Meanwhile, in the Democratic race, Hillary Clinton maintains her lead in Iowa, and Bernie Sanders is still ahead in New Hampshire.

In Iowa, she gets support from 47 percent of Iowa caucus-goers, while Sanders gets 36 percent and Martin O'Malley gets 4 percent.

That's essentially unchanged from a month ago, when the poll showed Clinton ahead of Sanders by an identical 11 points, 48 percent to 37 percent.

But Clinton's lead shrinks to five points when Vice President Joe Biden is added to the field - Clinton at 33 percent, Sanders at 28 percent and Biden at 22 percent.

And in New Hampshire, Sanders leads Clinton by nine points, 48 percent to 39 percent. That's essentially unchanged from a month ago, when Sanders was ahead 49 percent to 38 percent.

Yet once again, Clinton loses ground when Biden is added to the contest - Sanders sits at 42 percent, Clinton at 28 percent and Biden at 18 percent.

The NBC/WSJ/Marist polls were conducted Sept. 23-30. In Iowa, 431 potential GOP caucus-goers were interviewed (margin of error plus-minus 4.7 percentage points), as well as 348 Democratic caucus-goers (plus-minus 5.3 percentage points. In New Hampshire, 450 potential GOP primary voters were interviewed (margin of error plus-minus 4.6 percentage points), as well as 404 Democratic voters (plus-minus 4.)