Mitt Romney shakes hands with a boy during a campaign stop in Derry, N.H., on Saturday, the same day he was declared a winner in Wyoming. ((LM Otero/Associated Press))

Former Massachusetts governor Mitt Romney sealed his first victory in the Republican presidential race on Saturday, winning the Wyoming caucuses.

Romney won eight of the first 11 delegates chosen at county conventions held across the western state, while candidate Fred Thompson won two and Duncan Hunter won one.

One more Wyoming delegate was still to be chosen, but regardless of the outcome, Romney has won enough delegates to be declared the winner in the state.

The win is a boost for Romney, who lost to former Arkansas governor Mike Huckabee in the Iowa caucus on Thursday.

Republicans in the state appreciated the fact that Romney campaigned in Wyoming, which has little political pull in the presidential race. Huckabee did not visit the state, and neither did prominent Republicans like Arizona Senator John McCain and former New York Mayor Rudy Giuliani.

"Number one, he campaigned here," Leigh Vosler, a delegate, said of Romney. "I think that helped while some other candidates ignored us. But also he's the right person for the job."

Hunter, a California congressman, and Thompson, a former Tennessee senator, also campaigned in Wyoming, as did Texas Representative Ron Paul.

Wyoming held its caucuses earlier than usual this year, in January instead of March, in the hopes that the state could garner more attention by being between the first two big races — Iowa and New Hampshire, which holds its primary on Tuesday.

Tom Sansonetti, the county convention organizer, maintained Saturday that moving the state's caucuses ahead was the right thing to do.

"The ultimate goal is not how many times we appear on Katie Couric," Sansonetti said. "The ultimate goal was to have attention paid to rank-and-file Republicans by national candidates."

But Wyoming Republicans were penalized for holding their caucuses in January, as Republican rules state that nomination contests must be held after Feb. 5. The Republican National Committee cut in half the number of delegates Wyoming can send to the party's national convention in September, from 28 to 14.

Iowa is not being penalized because, technically, its caucuses are not binding on convention delegates.

While 12 delegates were chosen Saturday in Wyoming, the state will name its remaining two delegates at a statewide convention in May.

The Democrats will hold their caucuses in Wyoming in March.

Candidates square off in New Hampshire debates

The caucus results emerged a few hours before the Republican candidates held a heated 90-minute debate in Manchester, New Hampshire, in advance of the much-anticipated primary in that state.

Romney, Huckabee and McCain dominated the 90-minute debate, arguing against each other over issues like foreign policy and immigration. Giuliani and Paul also shared the stage, but were largely eclipsed by the other candidates.

The Democrats also held a debate in Manchester, with Senator Hillary Rodham Clinton going on the attack against rival Barack Obama, who won the Iowa caucuses. Clinton, once considered a front-runner, finished third behind Obama and former Senator John Edwards.

Clinton accused Obama of changing his positions on "a number of issues," including health care.

"You said you would vote against the Patriot Act. You came to the Senate, you voted for it. You said you would vote against the Iraq war, you came to the Senate and voted for [funding]," she said.

Obama rejected this description.

"I have been entirely consistent in my position," he countered, adding that he and Clinton have a philosophical disagreement over her proposal to require Americans to purchase health insurance or face a penalty from the government.

With files from the Associated Press