MANCHESTER, N.H. — Representative Ron Paul of Texas finished a strong second in the state’s Republican primary on Tuesday, which in many ways was the more telling outcome in a race where Mitt Romney’s dominance was never in doubt.

Mr. Paul polled well ahead of the late-surging Jon M. Huntsman Jr., who ran third, and Newt Gingrich and Rick Santorum, who battled for fourth. Mr. Paul benefited from the large turnout of independent voters, getting the nod from about a third, a little more than Mr. Romney. He also did well with young voters and those who said they were liberal on social issues.

But even if political analysts continue to regard the libertarian-leaning Mr. Paul as a protest candidate, with no shot at the nomination, his success here — on top of a third-place finish last week in the Iowa caucuses — means he will probably continue his campaign for months and perhaps to the summer convention.

“There is no way they are going to stop the momentum that we have started,” Mr. Paul told a raucous crowd shortly after Mr. Romney gave his own speech.