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Michael Kulma, a Korea specialist at the Asia Society, said the fact that Mr. Kim did not appear in public Tuesday was not necessarily an indication that he was incapacitated.

“There have been times in the past where he has gone missing, or fallen off the radar for up to a month at a time,” Mr. Kulma said. “But this may be different. … He is getting older, has diabetes and heart problems, and each of these grows more serious over time.”

Mr. Kim is known for his enjoyment of good food and wine. His former sushi chef, Kenji Fujimoto, was quoted by Bradley Martin in his book, “Under the Loving Care of the Fatherly Leader,” as saying that Mr. Kim had a wine cellar with 10,000 bottles in it and a fondness for shark’s fin soup.

The issue of succession is a major concern.

Mr. Chinoy said there were “question marks” about all of Mr. Kim’s three sons. “This is not a good time to have leadership uncertainty in North Korea,” he said.

A former U.S. official who dealt with North Korea and remains well-informed about the country said that rumors of Mr. Kim’s ill-health “seem a bit more intense than those of previous years.”

“That still doesn’t mean they are true,” he said.

The former official, who asked not to be named because he still has dealings with the North Koreans, said the United States should keep in mind that North Korea has remained “a remarkably stable place over the years, despite its erratic, dangerous and occasionally self-defeating policies,” including a famine that killed perhaps 2 million of the country’s 22 million people in the 1990s.

“Kim Jong-il’s health has not been good over the years, and one can’t help but think that the North Koreans, who prize the preservation of their system above all else, would have made plans to ensure that they would be able to put in place the new leadership that would allow them to do so. However, someday, perhaps soon, we will have to deal with the demise of the North Korean leader,” the former official said.

“This raises the question about whether our mutual isolation has left us more ignorant of the developments in the North than we should be, and less able to, perhaps, control events by reaching out to the next generation of leaders than we ought to be.”

  • Betsy Pisik at the United Nations and Barbara Slavin in Washington contributed to this article.