WASHINGTON — Mayor Giuliani’s hold on the front-runner’s perch in the Republican presidential nomination is eroding, with two new polls showing that Mitt Romney is opening up a widening lead in New Hampshire, site of the first primary.

While Mr. Giuliani has maintained his lead in national polls and in several state surveys, the former Massachusetts governor is now comfortably ahead in both Iowa and New Hampshire, two hotly contested early-voting states that have traditionally played a crucial role in determining the Republican nominee.

Mr. Romney opened up a 12-point lead over Mr. Giuliani in New Hampshire, 32% to 20%, in a Boston Globe/University of New Hampshire poll released yesterday. He leads in the state by 11 points in the latest Marist College poll, also released yesterday. Senator McCain of Arizona, who in an appearance yesterday on “Fox News Sunday” guaranteed a Granite State victory, is running third in both surveys.

The polls indicate that Mr. Romney has solidified his advantage and perhaps shifted the dynamic of the Republican race, after several surveys in September suggested Mr. Giuliani had closed the gap in New Hampshire. Mr. Romney has held a consistent double-digit lead since the summer in Iowa, where voters will cast the first presidential ballots in a caucus on January 3.

“Certainly he has to be seen as the front-runner now,” a political scientist and pollster at the University of New Hampshire, Andrew Smith, said yesterday of Mr. Romney.

For Mr. Giuliani, the latest slide comes as he has put renewed emphasis on winning New Hampshire, hoping to prevent a sweep of the first two contests by Mr. Romney. If Mr. Romney won both Iowa and New Hampshire, it would give him a significant jolt of momentum heading into Michigan, South Carolina, and Florida, which hold primaries later in January.

Compounding the former mayor’s problem is the recent federal indictment of a former New York police commissioner, Bernard Kerik, who Mr. Giuliani recommended to President Bush as a nominee for secretary of homeland security in 2004.

The Giuliani campaign downplayed the latest New Hampshire polls yesterday, pointing to a growing grassroots effort in the state as well as the fact that it has yet to run a single television ad there, while Mr. Romney has been on the air since May. “The polls are going to change a lot between now and the primary,” a Giuliani spokeswoman, Maria Comella, said. She also noted a statistic in the University of New Hampshire survey showing that 60% of state voters had yet to decide on a candidate.

Until recently, Mr. Giuliani’s strategy had focused heavily on the larger states holding primaries on February 5th, including New Jersey and California. He has held wide leads in polls in those states throughout the race, but analysts say that edge might not withstand the momentum Mr. Romney would gain nationally with victories in Iowa and New Hampshire.

“It’s not going to be the February 5th states,” Mr. Smith said. “It’s going to be over by then.”

Mr. Giuliani has increased his travel to Iowa and New Hampshire recently, but in states where face-to-face campaigning is held in high regard, he has been nowhere near as visible as Mr. Romney. Mr. Giuliani has held fewer than one-third the number of events in Iowa that Mr. Romney has held, according to a candidate travel tracker on the Web site of the Washington Post. And Mr. Romney has made about 50% more campaign stops in New Hampshire than Mr. Giuliani.

For months, Mr. Giuliani’s lead in national polls has fed his front-runner status, albeit in a race that is universally considered to be wide open, with Mr. McCain, Fred Thompson, and, increasingly, a former governor of Arkansas, Michael Huckabee, showing significant support. The Romney campaign counters that those surveys are based on little more than name recognition and thus are largely irrelevant.

“The term ‘national front-runner’ and fifty cents won’t even get you a cup of coffee nowadays,” a spokesman for Mr. Romney, Kevin Madden, said. “Mayor Giuliani keeps hanging his hat on national polls that show him getting around 30% support, yet fully 100% of the electorate knows who he is. That is a very big gulf to have between the number of voters that know him and the number that support him.”

Perhaps seeking to lower expectations, Mr. Madden cautioned that polls in the early states would “show a tighter race as the calendar progresses,” but he said the campaign was pleased to be in a strong position.

If there is any good news for Mr. Giuliani, it is that polls showing Mr. Romney comfortably ahead in Iowa and New Hampshire will lower expectations for Mr. Giuliani’s own performance, potentially dulling the impact of a Romney win. But that doesn’t mean the Giuliani campaign will easily relinquish the “front-runner” distinction. “There is no benefit in not being the front-runner now. You want to be the front-runner,” the interim dean of Boston University’s College of Communication, Tobe Berkovitz, said, though another school of thought holds that front-runner status turns a candidate into a target for negative campaigning and press coverage.