From the moment he became president, Dwight D. Eisenhower barely spoke to Harry Truman. Franklin Delano Roosevelt practically banned Herbert Hoover from the White House. Gerald Ford and Jimmy Carter were the best of friends, but only after both left office; they bonded on a long plane flight to Cairo, when Ronald Reagan sent them to the funeral of Anwar Sadat.

And George W. Bush has telephoned Bill Clinton on a regular basis over the last several years — a discovery that might shock Americans who remember well how Mr. Bush accused Mr. Clinton of dishonoring the Oval Office. That such conversations occurred has not previously been reported, but according to one person familiar with their frequent exchanges, the two swap stories about politics and engage in “presidential small talk.”

For more than a century, Washington has referred to the Senate as “the world’s most exclusive club.” But Americans were reminded last week that presidents have a club of their own, albeit one that rarely meets. With only a handful of living members at any given time, the Presidents Club sometimes looks more like a dysfunctional family than a collection of august world leaders. Old resentments bubble up, nobody seems to want advice from their elders, and they see one another mostly at funerals.