Nelson Mandela's memorial service wrought an unusual truce Tuesday across the faultlines of US presidential politics.

A current, a past, and a possible future US president crowded aboard Air Force One for the 16-hour flight from Washington to South Africa.

Barack Obama, George W. Bush and Hillary Clinton have had their share of political spats but had plenty of time to swap political gossip in the plane's conference room.

Obama and his wife Michelle, making the most of their current lease of the iconic blue and white presidential jet, were berthed in the plush cabin up front.

Bush and his wife Laura were in the medical suite behind Obama's office, while Clinton, accompanied by her globe-trotting aide Huma Abedin, camped out in the senior staff quarters.

While aiming to project cordiality in public, Bush and Obama are not exactly close. Privately disagreements still fester over the Iraq war.

Obama had branded the conflict launched by Bush as a "dumb war", and built a career opposing it.

There are many former officials in the Republican camp, meanwhile, who are angry that Obama did not reach a deal with Iraq to leave some US soldiers behind after his troop withdrawal, and they partly blame the president for the country's current violent torment.

Bush though, unlike his voluble former vice president Dick Cheney, has made good on his vow not to snipe at Obama from the sidelines and tells anyone who will listen that he is glad to be done with politics.

There is common ground between the pair on African soil however : Obama has singled out Bush for praise over his multi-billion dollar emergency plan to battle HIV and AIDS.

Obama, Clinton and Bush were joined in South Africa by two other US presidents -- Bill Clinton and Jimmy Carter -- who had their own share of spats when Clinton was in office.

Clinton and Obama have not exactly seen eye-to-eye over the younger Democrat's presidency: the scars of Obama's bitter 2008 primary campaign took a long time to heal.

The recent book "Double Down" which charted Obama's 2012 reelection campaign, revealed that at one point the president struggled to tolerate Clinton for a whole round of golf.

"I like him ... in doses," Obama is reported to have told an aide.

The relationship between the only two-term Democratic presidents since World War II took a turn for the better however when the president unexpectedly chose Hillary Clinton as his first secretary of state.

Then, Bill Clinton threw himself wholeheartedly into Obama's re-election campaign, winning the president's gratitude.

No event featuring Hillary Clinton these days is free of rampant speculation about whether she will take another tilt at the presidency in 2016 -- she remains the hot favourite for the Democratic Party nomination.

Each of the former presidents had a distinct relationship with Mandela.

For Obama, he was a distant political hero, who inspired him to take up activism when he was a student.

Mandela and Obama met in Washington before the younger man made it to the White House.

But the much anticipated meeting between the first black presidents of South Africa and the United States never happened, as Mandela was too sick to accept visitors when Obama was in the country in June.

For Clinton, Mandela was a trusted confidant at his hour of greatest need -- when he was under withering fire from political opponents over his affair with White House intern Monica Lewinsky.

Bush felt the lash of Mandela's tongue -- as the then retired South African president railed against the impending Iraq war in 2003.

Mandela was in prison for the entirety of Carter's 1977-1981 presidency.

But the two men came to know one another as sage former statesmen in the Elders group, which was founded by Mandela.