Hillary Clinton returned to the campaign trail this week after the Democratic nominee recuperated from pneumonia and her physician pronounced her healthy and “fit to serve as president.”

Yet the fitness of both candidates remained a major issue in the race for the White House, with Donald Trump appearing on “The Dr. Oz Show” and also mocking his rival’s health woes. At least one poll showed widespread concern about Clinton’s health among voters. And a separate poll, released Friday, asked who Democrats believe should take her place “if the unthinkable took place, and Hillary Clinton was forced for health reasons to step down as the Democratic presidential nominee.”

To be sure, the Clinton campaign is not suggesting anything of the sort. But there is a procedure for the Democratic National Committee to choose a replacement — just as there is for replacing a Republican, as was reportedly discussed by GOP officials in early August. At the time, ABC News reported, senior Republican Party officials were so confused by Trump’s behavior that they were exploring how to replace him if he quit.

The Democratic Party’s charter allows a meeting to be called by the DNC to fill “a vacancy on the national ticket,” and for a new candidate to be chosen by majority vote of members.

The charter doesn’t say who should fill that vacancy. That means neither Tim Kaine, Clinton’s running mate, or Bernie Sanders, her Democratic-primary opponent, is the automatic choice. In fact, it could be someone else entirely, such as Vice President Joe Biden.

In a Rasmussen Reports poll released Friday, 48% of likely Democratic voters said her replacement should be Vermont Sen. Sanders if health issues forced her out of the race. Twenty-two percent said Biden should be the nominee and 14% opted for Kaine.

For either party, however, getting a replacement on state ballots would be more complicated — especially with fewer than two months remaining until Election Day.

Ballotpedia, an online encyclopedia of U.S. politics and elections, writes replacing a candidate’s name in late September could prove “challenging.” A party would likely have to look to courts to have their new candidates considered, given elapsed ballot deadlines.

Election officials in states have been known to show leeway on those deadlines, Ballotpedia says. But the opposing party could file lawsuits seeking to enforce state laws as they’re written.

By late October and early November, nearly all ballot certification deadlines have passed and voters in some states will already have cast their ballots, the encyclopedia notes.

Clinton and Trump, meanwhile, each sought this week to tell voters that their health was a non-issue that shouldn’t affect their eligibility to be president. On Wednesday, Clinton’s campaign released a letter from the nominee’s physician that concluded: “She continues to remain healthy and fit to serve as president of the United States.” Trump’s doctor said the Republican nominee is in “excellent physical health.”

Read:Campaign releases more information on Clinton’s health.