(FORTUNE Magazine) – They say lightning doesn't strike twice, but it sure did at McDonald's.

On April 19, CEO Jim Cantalupo died of a heart attack. The board smoothly handed the reins to president Charlie Bell, 43, but two weeks later the Aussie was diagnosed with colorectal cancer and underwent surgery. (Bell, who has remained CEO, said on May 10 that he was "recovering nicely.") In both cases the company has received high marks from investors for addressing the situation quickly.

But the double blow does raise good questions: Just how much should a company--especially one as large as McDonald's--know about its chief's health, and how much should it tell shareholders and employees? We expect our nation's leaders to get regular physicals--should we expect the same of our corporate bosses?

While executive-health programs like that offered by the Mayo Clinic have boosted enrollments over the past few years, only 22% of companies sponsor annual physicals for execs, according to a 2003 survey by the American Management Association. For some, that's not enough. "The board is responsible for understanding everything there is to know about any factor affecting the CEO's ability to handle or even stay in the job, and failure to do so is a violation of their duty as fiduciaries," says Nell Minow of the Corporate Library, a corporate-governance watchdog. "This is a wake-up call for every corporate-governance committee," adds Bruce Ellig, former VP of HR at Pfizer.

Unfortunately, there isn't a standard playbook to follow when the boss gets sick. When Tenneco CEO Mike Walsh learned he had a brain tumor in January 1993, he held a press conference the very next day. That same week Reginald Lewis, chairman of privately held TLC Beatrice, died the day after the company finally announced he had a brain tumor and had lapsed into a coma.

While the Americans With Disabilities Act prohibits employers from asking about a candidate's medical history, once a job offer has been made, the company may insist on a physical. Current employees, like Bell, may be asked only job-related questions. (McDonald's has said that Bell was not aware he had cancer when he took the job, although he had reportedly been feeling ill since late February.)

More often than not, "boards just don't bring [health issues] up," says longtime CEO headhunter Tom Neff. Nina Dixon, who serves on three boards, says that in the CEO searches she has conducted, "We assumed that if they looked healthy, they were."

In the end, given the limits of the law, boards and shareholders are dependent on executives' being honest about their health. You may not be able to ask, but you'd better hope your CEO is willing to tell.

--Matthew Boyle