DERRY, N.H. — Mayor Giuliani said yesterday that people should “leave my family alone” when asked by a New Hampshire woman why the Republican presidential candidate should expect loyalty from voters when he doesn’t get it from his children.

Mr. Giuliani has a daughter who has indicated support for Senator Obama, a Democrat, and a son who said they didn’t speak for some time. His ugly divorce from their mother, Donna Hanover, was waged publicly while Mr. Giuliani was mayor of New York. Mr. Giuliani has since remarried.

Answering questions at a townhall meeting, Mr. Giuliani was asked why he should expect loyalty from GOP voters when his children aren’t backing him.

“I love my family very, very much and will do anything for them. There are complexities in every family in America,” Mr. Giuliani said calmly and quietly. “The best thing I can say is kind of, ‘Leave my family alone, just like I’ll leave your family alone.'”

His comments were greeted with a smattering of applause from the audience of about 120 people. Mr. Giuliani urged them to judge him based on his performance as mayor and a federal prosecutor, and he launched into a list of his successes such as reducing crime and welfare and prosecuting organized crime figures and drug dealers.

The questioner, Derry mother Katherine Prudhomme-O’Brien, opened by thanking Mr. Giuliani for how he handled the September 11, 2001, attacks and introduced him to her 5-year-old daughter, Abby, who was playing on the floor next to the platform where Mr. Giuliani stood.

Ms. Prudhomme-O’Brien, 36, wasn’t certain about Mr. Giuliani’s answer.

“If a person is running for president, I would assume their children would be behind them.” she said. “If they’re not, you’ve got to wonder.”

She said the issue is a question mark that is “going to stay there for a lot of people.”

Mr. Giuliani mentioned his wife, Judith, when he answered a question about Alzheimer’s disease, saying she had helped raise money to fight the disease.

“We’ve been touched by it very close to our family, too,” he said. Mr. Giuliani focused on health care during the hour-long forum, saying that buying health insurance ought to be like buying insurance for cars or a home, with people buying their own policies with different deductibles and types of coverage.

Employers and the government “never buy precisely what you want: They buy what they think is generally good,” he said.

Mr. Giuliani wants to give families a $15,000 tax credit to buy insurance privately rather than through employers and he proposes that any money left over from the credit be kept in tax-free health savings accounts.

In South Carolina, Mr. Giuliani launched two radio ads focusing on illegal immigration and his record as mayor. The first spot outlines Mr. Giuliani’s plan to deport illegal aliens who commit crimes, bolster border protection and reiterates his belief that newcomers to America should learn English. His second spot highlights his work as mayor on cutting crime, trimming welfare rolls, and reducing taxes.