GEOFF BENNETT: Right on the heels of President Trump's state visit to China last week, Russia's Vladimir Putin stopped in Beijing for a meeting today with his chief ally, Xi Jinping.

As Nick Schifrin tells us, they focused on economic issues and criticizing U.S.

foreign policy.

NICK SCHIFRIN: Today in Beijing, fanfare and red carpets for two authoritarian leaders to trumpet their alliance.

At the Great Hall of the People, the ceremonial center of communist China, Xi Jinping met his closest ally, Russian President Vladimir Putin, for a synchronized show of power and celebration by China's youngest.

It was the exact same spot that Xi welcomed President Trump just six days ago, seemingly identical in its pomp and circumstance, although apparently not to President Trump.

DONALD TRUMP, President of the United States: I think it's good.

I don't know if the ceremony is quite as brilliant as mine.

I watched.

I think we topped him.

NICK SCHIFRIN: But even if the U.S.

and China pledge strategic stability, they remain rivals.

And China and Russia are strategically aligned, and today jointly criticized the U.S.... NARRATOR: Golden Dome for America.

NICK SCHIFRIN: ... for President Trump's proposed Golden Dome missile defense, which Russia and China today called a -- quote -- "obvious threat to strategic stability" for the expiration of the last U.S.-Russia arms control treaty, New START, and for the U.S.-Israel war on Iran.

XI JINPING, Chinese President (through translator): The world today is far from peaceful, with unilateralism and hegemonism posing profound dangers.

The world faces the risk of regressing to the law of the jungle.

VLADIMIR PUTIN, Russian President (through translator): Russian-Chinese relations have reached a truly unprecedented level.

ANDREW WEISS, Carnegie Endowment for International Peace: The split-screen image of chumminess between Vladimir Putin and Xi Jinping, and on the other hand Donald Trump's recent visit, could not be more stark.

NICK SCHIFRIN: Andrew Weiss is a former State Department official who's now with the Carnegie Endowment.

ANDREW WEISS: The Russians and the Chinese are absolutely essential partners to each other in the political sphere and in the economic sphere.

They are demonstrating in their rhetoric and in the imagery of today's visit deep apprehension about Donald Trump.

NICK SCHIFRIN: The day-to-day implications of that play out in Ukraine.

China provides what the U.S.

has said is 90 percent of Russia's microelectronic imports for weapons used in Ukraine and 70 percent of Russia's machine tool imports to make weapons for Ukraine.

ANDREW WEISS: Russia sees China as the key partner for what it's going to need to keep the war going, as well as for when it turns to rebuilding its military whenever the war ends.

NICK SCHIFRIN: But there are limits to what China and Russia have called their no-limits partnership.

Not announced today, a deal for a major pipeline that would take Russian natural gas to China.

ANDREW WEISS: China has tremendous negotiating leverage, and it's working to get the sweetest possible deal from the Russians.

And China, given the fact that this is a complex agreement that could last upwards of 30 years, is going to be extremely careful not to make impulsive, last-minute gestures just to score political points or to make Vladimir Putin feel good.

NICK SCHIFRIN: But Putin and Xi feel good about their alliance, which Putin called truly unprecedented and Xi called the highest level in history.

And so these two leaders, who maintain an axis of authoritarianism alongside Iran and North Korea, continue to confront the U.S., and Putin left China with a standing ovation.

For the "PBS News Hour," I'm Nick Schifrin.