The news last week that President Trump’s valet and Vice President Pence’s press secretary had both contracted the coronavirus sent a scare through the White House. While officials said both leaders subsequently tested negative, the episode raised a worrisome possibility: What happens if Trump or Pence is stricken—or, worse, if both became ill at the same time?

The result could be anything from a temporary disruption to a full-blown constitutional crisis with competing claims on the presidency. What’s critical, experts say, is that the identity of the commander-in-chief be clear in any situation. At least one scenario could arise where it wouldn’t be.

The degree of economic and geopolitical fallout would depend heavily on the severity of the illness, and especially on whether Trump himself became incapacitated, say current and former White House officials and outside experts. “There’s a protocol for everything,” says David Axelrod, former senior White House adviser to Barack Obama. “We routinely went through drills for what to do in case of terrorist or nuclear attacks, but I honestly never anticipated a pandemic situation like the one the White House is facing now.”

Markets would almost certainly drop on news of a presidential diagnosis, says Ian Bremmer, president of Eurasia Group, a geopolitical risk consulting firm. But he expects traders would take comfort from U.K. Prime Minister Boris Johnson’s recovery from his recent bout of Covid-19. Although Johnson deputized Foreign Secretary Dominic Raab to handle some duties when he entered intensive care on April 7, he never formally transferred power; Johnson has now returned to work and resumed his full slate of duties.

“If Trump were to get it and is quarantined in the residence, but stays in charge of the government and is tweeting like crazy, I think there’d be de minimis market impact,” says Bremmer.

Even if Trump became too ill for vigorous tweeting, there’s a process that past presidents have employed to temporarily relinquish power. The Constitution’s 25th Amendment allows Trump to hand over control to the vice president and then reclaim it as soon as he declares himself able. George W. Bush did this twice during his presidency, while undergoing medical procedures, and Ronald Reagan once, for colon surgery. If Trump were stricken suddenly or had to be sedated for intubation, the 25th Amendment also allows the vice president and cabinet to execute the transfer of presidential power.

In the grim—and statistically unlikely—case that one is needed, a road map also exists for what would happen if the president and vice president were both to pass away. “In that event, the line of succession is clear,” says Ilya Somin, a law professor at George Mason University. “House Speaker Nancy Pelosi would take over.”

But constitutional experts warn that chaos could ensue if both Trump and Pence were to become incapacitated by Covid-19, because the law provides little clarity on resolving such a scenario.

“It would be a real shit show that could result in a full-scale constitutional meltdown,” says Brian Kalt, a law professor at Michigan State University and the author of Unable: The Law, Politics, and Limits of Section 4 of the Twenty-Fifth Amendment. “It would immediately go to court, and they’d have to decide real quick what to do. Because not knowing who the president is even for a couple of hours could be extremely perilous for the country.”

If Trump and Pence were both unable to fulfill their duties, neither could invoke the 25th Amendment. The Constitution instructs Congress to legislate a line of succession, which was most recently updated in the Presidential Succession Act of 1947—the law that puts the speaker of the House of Representatives, Nancy Pelosi, next in line for the presidency. The trouble, Kalt says, is that the Constitution doesn’t offer a procedure for determining a president’s “inability” to perform, giving rise to the possibility of a dispute in which Pelosi, a Democrat, declared herself acting president even as Trump and Pence (or their lawyers) declared themselves fit to serve.

A succession dispute is hardly inconceivable. During Watergate, in the eight weeks between Spiro Agnew’s resignation and Gerald Ford’s confirmation, the vice presidency was vacant, putting Democrat House Speaker Carl Albert next in line for the White House. Albert vowed that if he were to ascend to the presidency, he would promptly appoint a Republican vice president and resign, rather than let his party appear to usurp power.

“That’s hardly a scenario you could count on today,” says Kalt, who has urged Congress to rewrite the succession law to put the Secretary of State (in Trump’s case, Mike Pompeo) third in line for the presidency.

The White House says there’s no reason for alarm. A spokeswoman said the federal government always has plans for continuity of operations, but declined to outline what the plan would be if Trump and Pence were unable to carry out their duties. Both are tested daily for the coronavirus.

Some White House officials have grown concerned that Trump, Pence, and their staffs have routinely intermingled in recent weeks, many of them without wearing a mask, thereby increasing the chances that both principals could get infected. “Pence should largely stay out of the White House as [Dick] Cheney did after 9/11,” says one former Trump official. So far, he has not (although he has been staying away from the president). After his press secretary, Katie Miller, tested positive on May 8, Pence skipped a weekend meeting between Trump and military leaders at the White House but returned to work the following Monday.

By contrast, Dr. Anthony Fauci, the director of the National Institute of Allergy and Infectious Diseases, and Dr. Robert Redfield, director of the Centers for Disease Control and Prevention, both went into self-isolation after coming into contact with a person at the White House who tested positive.

Throughout the crisis, Trump has resisted many of the precautions urged by public health officials. Advisers say he is determined to project an air of normalcy in hopes that this will convince Americans to leave their homes and begin spending money that will revive a U.S. economy devastated by the pandemic. His reelection may depend on it.

In fact, more than economic, geopolitical, or constitutional risk, the surest consequence of an Oval Office coronavirus diagnosis—or a double diagnosis—is that it would greatly increase electoral risk to Trump by smothering the already limited public confidence in his effort to reopen the economy. Even as many states take tentative steps to lift virus-related restrictions on businesses and public activities, a May 7 Pew Research Center poll found that a large majority of Americans (68%) say their greatest concern is reopening the economy too quickly. Only 31% worry about not lifting restrictions quickly enough.

With the virus now confirmed in the West Wing, Trump at a press conference on May 11 appeared to be more willing to take precautions, perhaps aware that a presidential infection could decimate his reelection hopes.

Trump claimed he’d had little recent contact with Pence, who has returned to the White House campus, but indicated that he might take additional steps to distance himself from his vice president. “He comes into contact with a lot of people,” Trump told reporters. “It’s something probably during this quarantine period, we’ll probably talk about. I have not seen him since then.” He added, “We can talk on the phone.”

Trump also said he issued an order for all White House staffers to begin wearing masks to help stop the spread of the virus inside the West Wing. But this stepped-up health measure has its limitations: It doesn’t apply to the president, who still doesn’t intend to wear a mask.