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Polls from Quinnipiac University of the crucial swing states of Florida, Ohio and Pennsylvania show Donald J. Trump and Hillary Rodham Clinton holding solid leads going into the next round of presidential debates.

The surveys, released on Wednesday, show that Mr. Trump has expanded his leads in Florida and Ohio, and has seen some slight tightening in Pennsylvania since August. Despite a lackluster debate performance last month, the billionaire developer continues to lead rivals such as former Gov. Jeb Bush of Florida, Senator Marco Rubio of Florida and Gov. John Kasich of Ohio in their home states.

“Those who were waiting for Donald Trump’s campaign to collapse will need to wait longer – at least in the three key states of Ohio, Florida and Pennsylvania,” Peter A. Brown, assistant director of the Quinnipiac University Poll, said in a statement.

The polls show Ben Carson, the retired neurosurgeon, trailing Mr. Trump in second place in all three states and they indicate that Mr. Rubio, of Florida, is also on the rise.

On the Democratic side, Hillary Rodham Clinton holds dominant leads against Senator Bernie Sanders of Vermont and the undeclared Vice President Joseph R. Biden Jr. in Florida and Ohio. She leads them both handily in Pennsylvania, too, although Mr. Biden has gained some ground in the state where he was born.

The polls, which have a margin of error of five percentage points, show that Mr. Biden does the best among the Democrats in the swing states when matched up against the leading Republican candidates. Mr. Trump, on the other hand, fares the worst in general election matchups.

“Trump, despite his strong showing in mock Republican primaries, fares worst among the G.O.P. candidates matched against the three Democratic aspirants – giving some credence to pundits who say the billionaire could be every Democrats’ favorite G.O.P. nominee,” Mr. Brown said.