Last year, Trump abruptly hung up on then-Australian Prime Minister Malcolm Turnbull after an immigration dispute. But the Australian Embassy shrugs that moment off as just a blip as it celebrates “100 years of Mateship” this year, harking back to World War I battlefields where troops from the two nations fought and died beside one another.

Never mind the insults Trump has lobbed at Canadian Prime Minister Justin Trudeau. Canada has dispatched members of Parliament and the cabinet on hundreds of trips south to find ­common cause with U.S. governors, state legislators and mayors on issues such as trade and climate change.

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Long-standing allies whose leaders have sometimes had testy relations with Trump are increasingly keeping ties with the United States alive in ways that bypass the White House.

Faced with Trump’s volatility, a foreign policy that is constantly changing, and many vacancies in the State Department and other traditional venues for communication, some governments are employing what diplomats call the “doughnut strategy.”

“What many, many foreign governments are doing is trying to find ways to get around the problem,” said Nancy McEldowney, a former director of the Foreign Service Institute, which trains U.S. diplomats, and now a professor at Georgetown University. “When you have a problem in the middle, you work around it by building out a network that encircles the problem.”

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The efforts to contact local and state governments, business leaders, and civil society reflect the conviction that the United States is still an influential player in the world. So even countries that hoped to lie low until a new administration is in place have concluded that they can’t afford to do that. Some are already gaming scenarios for how to deal with a second Trump term.

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In the meantime, some countries are making creative connections with Americans, far from the traditional halls of power in Washington. Germany is focusing on culture and heritage in its Wunderbar Together campaign, with a database for an estimated 50 million Americans who can trace their lineage to Germany. It is holding 1,000 events in every region of the United States in the next year, commemorating the 30th anniversary of German reunification. Last week, a German breakdance troupe, the Flying Bach, performed in front of the Lincoln Memorial.

German officials swatted aside questions about whether the campaign has anything to do with the Trump administration, saying the United States is just the latest in a string of countries where they have held Wunderbar Together celebrations. But before he left Bonn for Washington last week, German Foreign Minister Heiko Maas acknowledged the differences between the two governments’ views on the Iran nuclear deal, climate change, trade and NATO military spending.

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“Things that used to be taken for granted are no longer that way; they must be worked on,” he said.

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Canada is taking a less public approach, enlisting cabinet members and business executives to make official visits to the United States.

“There’s no question we are upping our game since things became uncertain in our priority areas, like trade relations,” a ­Canadian official said of the uptick in official visits. “They are capable of engaging with the administration and Congress on our behalf.”

Early in the Trudeau-Trump relationship, Canada tried a charm offensive stressing the importance of the connection, said Laura Dawson, director of the Canada Institute at the Wilson Center. But that proved insufficient during NAFTA negotiations and, ultimately, with tariffs that Trump imposed in the name of national security.

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Invoking national security deeply offended many people in a country that helped U.S. diplomats escape from Iran in 1979, welcomed passengers grounded in Newfoundland after the 2001 terrorist attacks and sent troops to Afghanistan.

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Colin Robertson, a former Canadian diplomat who was posted in Washington, said Canada has come to realize it is not enough to train diplomacy only on the White House and Congress.

“The Trump administration is changing the game,” said Robertson, who now studies U.S.-Canadian relations at the Canadian Global Affairs Institute. “There’s a growing recognition we have to play the American system the way it was designed, with checks and balances, a separation of powers. Not just at the congressional level, but the role governors and state legislators play.”

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Some countries are bringing forth a heavy dose of nostalgia.

Australia has largely escaped Trump’s ire since his hang-up call with Turnbull.

“Perhaps most crucially, the government has gone into overdrive trying to educate Trump on the history of shared military sacrifice over the last 100 years,” said James Curran, who teaches history and foreign policy at the University of Sydney.

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Australia’s “100 Years of Mateship” is rooted in the centennial of the Battle of Hamel, a fight along the Western Front in which U.S. and Australian soldiers fought in Le Hamel, France. The idea of the Australian ambassador in Washington, the campaign came with a TV documentary, badges, stickers, posters and even a “mate ale” brewed in Texas.

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“It is as if the government here thinks that the more it reminds the U.S. of how much we’ve been there for them on the battlefield, then they will surely come to help us in the event of a future military crisis,” Curran said. “But I wonder: Is anybody there in the White House or State Department really listening to these Australian clarion calls about ‘mateship’? After all, there is the old saying that ‘when you are living and working in Washington, you need to have very good peripheral vision to see Australia.’ That surely is intensified in Trump’s Washington.”

As foreign governments seek to get Americans to reflect on decades of friendship and mutual values, the historical reminiscences and cultural events represent a role reversal. A decade ago, U.S. diplomats worried that a new generation of Europeans did not appreciate how the United States had come to the continent’s aid during World War II and the Cold War.