Newt Gingrich is passing Mitt Romney in the battle for the Republican presidential nomination, an average of national polls shows, while third-place candidate Herman Cain tries to fight off yet another allegation about his sexual relations with women. Gingrich, the former speaker of the House of Representatives, has surged ahead in the Republican contest to challenge President Barack Obama. Meanwhile Cain, a former pizza chain executive, has watched his favorable numbers decline steadily since he was hit with sexual harassment allegations this month by women who worked for the National Restaurant Association when he ran the trade group in the 1990s. Gingrich, who has seen his political standing rise as he has posted solid debate performances, has become the latest challenger to Romney, whose poll numbers have dipped slightly. The Real Clear Politics average of four national polls shows Gingrich with an advantage of 2.5 percentage points over Romney. Gingrich has rebounded from his campaign’s near collapse this summer, when much of his staff resigned. So far Rep. Michele Bachmann, Texas Gov. Rick Perry and Cain have made a serious run at Romney before falling from favor and quickly drifting out of contention as deeply conservative Republican primary voters search for an alternative to Romney, the former Massachusetts governor and venture capitalist. Many conservatives view him as too moderate and weighed down by a history of shifting his positions on issues held dear by the party’s base. Gingrich, after focusing his fire on Obama, has begun attacking Romney, branding him as a political opportunist. “We think there has to be a solid conservative alternative to Mitt Romney,” Gingrich said Monday. The latest embarrassing claim against Cain erupted Monday when 46-year-old Ginger White said she and Cain, who is married, had a 13-year affair that ended shortly before he began his run for the nomination. “It was fun,” said White, as she described in an interview with an Atlanta, Georgia television station how Cain had bought her plane tickets for a rendezvous in Palm Springs, California. “It was something that took me away from my sort of humdrum life at the time. And it was exciting.” On Tuesday, Cain vowed to continue his presidential campaign despite the allegation of the extramarital affair. A campaign spokesman said “yes” on Tuesday when asked whether Cain was definitely staying in the race. Cain went on television to deny White’s claims even before the report aired. It was a faster and more deliberate response than he had managed when it was reported that three women alleged he had sexually harassed or groped them when he was the head of the restaurant association. The trade group paid settlements to two women who had worked there. “Here we go again,” Cain told CNN as he denied White’s accusation. “I didn’t do anything wrong.” His lawyer separately issued a statement that did not deny the affair with White but blamed the news media for wrongly reporting the conduct of consenting adults. Cain has indicated he will stay in the race so long as he has the support of his wife, but the latest allegations could ruin any last chance of reclaiming a top spot among the seven candidates vying to overcome Romney. Cain avoided reporters and their questions when he attended a fundraising event Monday night in the Virginia suburbs of Washington. That may be more difficult Tuesday, when he is scheduled to speak to students at Hillsdale College in Michigan, or Wednesday, when he is scheduled to begin a bus tour through Ohio. Cain surged in the polls while pushing his flat tax plan and providing tough criticism of Obama during televised debates. But as the harassment stories surfaced, Cain also stumbled in explaining his views about US policy toward Libya and other foreign policy issues, creating an opening for rival Gingrich to assert himself as a more reliable, seasoned politician to challenge Romney and even Obama. After the initial report and Cain’s denial, White told The Associated Press that Cain was not being truthful when he said there had been no affair. In its report, the Atlanta television station said White had Cain’s name in her mobile phone contacts, and when its reporter sent a text message to the number, Cain called right back. Cain said White had his number because he was trying to help her financially. In her interview, White said she decided to come forward after seeing Cain attack his other accusers in an appearance on television. White told the Atlanta TV station she expects to be scrutinized by Cain and the media. Georgia court records show a series of judgments against White for not paying rent in Atlanta-area apartments, including one filed about two weeks ago. She also faced a libel suit as part of a larger business dispute with a former business partner.