U.S. Secretary of State Rex Tillerson, right, meets with Chinese State Councilor Yang Jiechi before their meeting at the State Department on Feb. 28. (Yuri Gripas/Agence France-Presse via Getty Images)

For China’s Communist Party, it’s hard to know whether to laugh or cry.

Hardly a day goes by without some opinion piece in state media here reveling in the demise of ­democracy and American global leadership under President Trump. 

But underneath the triumphalism, China’s government is deeply anxious, experts say, as it faces a government packed with hawkish voices led by man who sees Beijing as one of the United States’ fiercest competitors.

On Monday and Tuesday, China’s most senior diplomat, State Councilor Yang Jiechi, was in Washington for a visit — which included a brief meeting with Trump — aimed at finding a new basis for what former president Barack Obama called the most important bilateral relationship of the 21st century.

It won’t be an easy task.

Economic and business ties had long been the ballast that kept the relationship stable, but they have now become sources of conflict. Climate change had provided a narrative of cooperation rather than competition, but it has been taken off the table. Meanwhile ­tensions over North Korea’s nuclear program, the disputed ­waters of the South China Sea and the status of Taiwan loom larger than ever.

“China is keen to find something to replace climate change as the notional glue to hold the relationship together,” said Christopher Johnson, a former senior CIA China analyst and now an expert at the Center for Strategic and International Studies.

“But what really keeps the relationship from tipping into an adversarial one is the economic relationship,” he said. “If that gets scratchy, the whole stability of the relationship becomes impacted.”

It is not unusual for new presidents to face tough adjustment periods when it comes to China policy — Ronald Reagan clashed with Beijing over Taiwan, Bill Clinton over human rights — but with Trump it is “qualitatively different,” said Evan Medeiros, formerly Obama’s chief adviser on Asia and now the Eurasia Group’s ­managing director for Asia

“The current agenda of potentially contentious issues is quite large,” he said. “Plus this administration appears to be packed with senior officials who have an ideological and/or an interest-based concern about China and see it as a strategic competitor, and a ­president who, to the extent he has a coherent view about China, ­appears antagonistic.”

Indeed, the past three months have been a roller-coaster ride for the Chinese. 

Exultation greeted Trump’s victory, just as it did in Moscow — here was a business executive and a dealmaker, the argument went in China, a man who won’t try to subvert our regime by promoting democracy, like Hillary Clinton might have done. 

But the mood soon turned to horror as Trump reached out to Taiwan and questioned the principle that there was only one China, the bedrock of diplomatic ties between Washington and Beijing. 

But Beijing stood firm, and Trump appeared to back down, finally agreeing to honor the one-China policy in a “very warm” phone call with Chinese President Xi Jinping.

Lines of communication ­between the two governments, previously somewhat scarce, opened up: Secretary of State Rex Tillerson met Chinese Foreign Minister Wang Yi in Munich, while Treasury Secretary Steve Mnuchin spoke with China’s ­economic leaders.

Collision course avoided, proclaimed the China Daily newspaper, as China and the United States “restore belief that they can reduce frictions.”

There was a sense, too, that the administration’s more radical impulses toward China, personified by National Trade Council chief Peter Navarro, are being tempered by an array of more conventional figures from the conservative establishment, such as Defense Secretary Jim Mattis, Tillerson or the Goldman Sachs duo of Mnuchin and Trump’s chief economic ­adviser, Gary Cohn.

“These guys have got to deal with the real world as it is,” said Douglas Paal of the Carnegie Endowment for International Peace. 

“I tend to see this as a contest between the deep state — the old poles of intelligence, State, ­Defense and Congress — trying to keep the ship of state floating when there are a lot of other ­people trying to rock the boat,” Paal said. 

An early sign of this moderating influence came when Mattis visited Tokyo and Seoul, and stressed diplomatic rather than military solutions to the dispute in the South China Sea. 

Another indication: While Trump told Reuters last week that the Chinese were the “grand champions” of currency manipulation, Mnuchin was telling Bloomberg News that any decision to label China a manipulator would only follow a review by the Treasury Department.

Nevertheless, there is a widespread belief that the administration will unveil a package of trade and investment measures aimed at China when (and if) Robert E. Lighthizer is confirmed as U.S. trade representative.

He and the new commerce ­secretary, Wilbur Ross, are ­expected to take a tough line with China on trade, while Mnuchin told ­Chinese officials he wanted “a more balanced bilateral economic relationship.”

Although the business community has been lobbying hard against Trump’s most radical ­proposals, reciprocity is now the buzzword in Washington. Why should China’s subsidized state-owned ­giants get a pass to export to and invest in the United States when China erects barriers the ­other way? 

“Brace for U.S.-China trade ­conflict,” the analysis firm Gavekal Dragonomics said in a client ­report, warning that the coming months will probably bring ­“aggressive trade actions” by the United States and a firm Chinese response.

The best outcome, it argued, is that Trump’s “get tough” approach wins some cosmetic ­concessions from China, before the two sides resume more-productive talks. “The worst outcome is that the Trump administration gets trapped by the fantasy it can simply force China to change, and the world gets stuck with a ­full-scale trade war.”

War isn’t likely in the South China Sea, but tensions could ­easily rise again, with Trump promising a big increase in naval spending and voices in the Pentagon arguing for a greater U.S. ­naval ­presence there, experts said. China, meanwhile, appears to be continuing its slow, steady ­construction of military facilities there, with buildings that U.S. ­officials say could one day house surface-to-air missiles.

North Korea is another point of tension, with the recent assassination of leader Kim Jong Un’s half brother in Malaysia, apparently with a VX nerve agent, a reminder of the regime’s ruthless nature. 

“The mood in Washington is that the administration is more open to thinking about military options than in the past,” said Medeiros. In other words, “taking the kinds of military actions, like joint exercises and missile defense, that China is very uncomfortable with.”

On Monday, China’s Foreign Ministry again signaled its firm resistance and strong dissatisfaction with plans to deploy a U.S. missile defense system in South Korea, warning that both countries would bear the consequences.

On the global stage, China has been nimble in reacting to Trump, reaching out to Germany and the European Union, which have been deeply hurt by Trump’s rebuffs, or, as Xi did in Davos, Switzerland, presenting Beijing as a somewhat unlikely defender of “economic globalization.”

But when it comes to U.S. relations, Beijing has been outmaneuvered so far by Japanese Prime Minister Shinzo Abe, who stole a march on his Chinese rivals with a round of golf and a visit to the president’s Florida home, Mar-a-Lago.

At the American Enterprise Institute, Daniel Blumenthal said that Trump has been smart to rock the Chinese back on their toes, adding that it is time for a tougher approach on everything from the economic relationship to the South China Sea and Taiwan. 

Walter Lohman of the Heritage Foundation welcomed Trump’s commitment to the military, saying that a bigger Navy is crucial to defending U.S. security interests in Asia’s waterways.

But others said that Trump could be tipping the relationship with China into a new period of contention and conflict that won’t help anyone

“Uncertainty is okay, I don’t have a problem with that,” said Johnson. “But too much uncertainty and unpredictability becomes scary to China and, perhaps more importantly, to our allies. It requires a lot of nuance and skill to walk that line finely.”