They did not think much of each other at first. They crisscrossed the country for months, warning voters that the other one should not be trusted with power. Their campaign was as bitter as any of the era and ended in one of the closest elections in modern times.

And then, against all odds, against all political logic, Jimmy Carter and Gerald R. Ford actually became friends.

Not friends in the Washington sense, where someone talks on the floor of Congress about “my friend from the state of Georgia” before stabbing them in the back. Real friends. Friends who commiserate on the phone over shared struggles. Friends whose wives and children become close. Friends who see a like-minded soul. Friends who speak at each other’s funerals.

The unlikely bond between Mr. Carter and Mr. Ford is a rare story in the history of the American presidency and all the more unimaginable in today’s polarized environment, but it transcended politics and partisanship. The two men who clashed in the 1976 election eventually became so tight that they made a pact that when one of them died, the other would give a eulogy. Mr. Carter did that for Mr. Ford in 2007. Now, in a way, Mr. Ford will return the favor on Thursday.

While he did not survive to honor his successor in person, Mr. Ford left behind a written eulogy before he died and it will be read at Mr. Carter’s service at Washington National Cathedral by Steven Ford, the former president’s third son. Walter F. Mondale, who was Mr. Carter’s vice president, likewise left behind a eulogy before his own death to be read by his son Ted Mondale.