The two families who have competed at the apex of American politics for the past two decades joined Thursday to pay tribute to the opening of George W. Bush’s presidential center.

Whether they will face off again in 2016 was the unspoken subtext.

President George H.W. Bush, frail and seated in a wheel chair, beamed with pride, thanking the audience for honoring “our son.” President Bill Clinton, who defeated the elder Bush 20 years ago, joked that he had become the “black sheep son” of the Bush family.

George W. Bush, standing before his gleaming new center, observed that it was the “first time in American history that parents have seen their son’s presidential library.”

But amid the camaraderie and celebration were two reminders of the fight that could lie ahead: former first lady Hillary Rodham Clinton, who accompanied her husband on stage, and former Florida Gov. Jeb Bush, who sat in the audience with his wife, Columba.

Both are considering presidential bids in three years, moves that could create unprecedented dynasties — the first spouses to serve as president or the first brothers — and lead to a similar event at a future library a decade or more from now.

President Barack Obama, who broke the 20-year string of either a Bush or Clinton in the Oval Office, thanked his predecessors, noting that the “world’s most exclusive club” acted more like “a support group” of former presidents who help each other. Obama has his own back story with the families — he waged a long primary race against Clinton in 2008, campaigned vigorously against Bush’s policies and then turned to the former first lady to run the State Department. When Obama needed a re-election boost last year, Bill Clinton was there to help.

Indeed, the White House has created a bond among the families.

“The presidents’ club is small,” said Mary Matalin, a longtime adviser to the Bush family. “Only presidents who have sat behind that desk in the Oval Office know the weight of it. There’s just a bond there that nobody else can understand except for a handful of people who have done it.”

The families first squared off in 1992, when George H.W. Bush ran for re-election and faced Bill Clinton and independent H. Ross Perot in a riveting campaign as a recession eroded his his sky-high approval rating following the first Iraq war.

Clinton repeatedly questioned Bush’s handling of the economy while the incumbent challenged the fitness for office of Clinton and running mate Al Gore, punctuated by Bush’s claim that his English springer spaniel, Millie, knew more about foreign policy “than these two Bozos.”

George W. Bush served as an aide to his father’s re-election campaign, giving him a close-up view of his father’s defeat — and plenty of reasons to dislike the opponent. But the harsh words quickly subsided.

When the Clintons arrived at the White House in January 1993, aides to both families said the Bush family was gracious to the new president and his family. The elder Bush avoided criticizing his successor and after Clinton’s presidency, the two joined forces to raise money for victims of the devastating tsunami in Asia in 2005 and Hurricane Katrina in 2006.

Aides describe a friendship between the two ex-presidents that almost resembles a father-son relationship. “My mother told me not to talk too long today — and Barbara, I will not let you down,” Clinton quipped Thursday.

That friendship helped connect Clinton and George W. Bush, who campaigned for president in 2000 on restoring “honor and dignity” to the White House following Clinton’s impeachment over a sex scandal. After Haiti’s devastating earthquake in 2010, Obama tapped Clinton and the younger Bush to lead the relief effort.

Joshua Bolten, a former chief of staff to George W. Bush and a board member of the Clinton Bush Haiti Fund, said the relationship between Clinton and the elder Bush “helped open the door to a good 42 and 43 relationship.”

Both families know what it’s like to watch a family member face the scrutiny of a national campaign. Clinton recounted that in 2008, a time when George W. Bush’s approval ratings sank and Republicans avoided him, he and the lame-duck president would talk politics by phone as Hillary Clinton sought the White House.

Clinton, standing a few feet from Obama, joked that a “chill went up and down my spine” when he learned that the Bush library’s records were digitized. “Dear god I hope there is no records of those conversations.”

The two families could be thrust into the spotlight once again if Hillary Clinton or Jeb Bush runs for president in three years.

Expectations are growing for both of them three years before the next election. Clinton supporters chanted her name outside her private speech in nearby Irving, Texas, on Wednesday night while Jeb Bush received encouragement to run for president during an event with a Dallas civic group.

And it may not end there,. Looking to the future, Jeb Bush pointed to the nascent campaign in Texas of yet another potential member of the family dynasty: his 37-year-old son, George P. Bush.

“To be honest, I’m focused on the land commissioner race in 2014,” Bush said with a smile.