YAVORIV, Ukraine — The clatter of rifle fire, the thud of mortars, and the thunder of grenades echoed across this military training ground near the Polish border.

It was nothing that many of the Ukrainian soldiers arriving here hadn’t heard before in the eastern regions of their country, and it was familiar music, as well, to the Americans who have come here to try to make them even better fighters.

The Ukrainians brought stories from the front about the enemy, the arms, and the firepower used against Ukrainian troops. For American soldiers, listening to these members of former Soviet forces talking about their adversaries, also from the former Soviet army, this has been an education. It has given them a chance to study in granular detail a great deal about the evolution of Russian combat forces in the last quarter-century.

Indeed, U.S. troops and Ukrainian troops learning from each other seems to be just the kind of thing that Russian President Vladimir Putin was worrying about when he called an emergency meeting of his security council on Wednesday.

As the pace of fighting in eastern Ukraine picks up (with each side blaming the other, as usual), one of Moscow’s stated concerns is about Ukraine’s new defense doctrine, officially released this week.

Russian Security Council Secretary Nikolai Patrushev told journalists it “provides the United States and NATO with an opportunity to use Ukraine’s resource base and provokes further escalation in the southeast of the country.” Kiev’s doctrine includes major military reforms and names Russia as the most dangerous enemy. The U.S., British, Polish, Canadian, and other NATO military forces drilling with Ukrainian forces this summer are a strong signal for Putin and his closest circle that the West is ready to be involved in a military conflict. They may also give him a pretext to raise the stakes in Ukraine’s eastern region, known as Donbas.

Rival exercises in other areas by NATO and the Russians represent the biggest buildup in military tensions with Moscow since the Cold War, according to many analysts. And Putin seems to relish the confrontation, even when his security cabinet recommends caution.

“The situation is very tense and concerning,” independent analyst and former Kremlin adviser Stanislav Belkovsky told The Daily Beast on Wednesday. “Putin is ready to fight with NATO, as he seriously believes that the U.S. wants to occupy Russia.”

Among the 10 members of his Security Council, “Putin is the only one who is convinced that all of his men are ready to die for him; so far he can see that with the death toll of Russian recruits growing in Donbas, Russians have not been out protesting against the war,” Belkovsky said.

Russian opposition leader and former KGB officer Gennady Gudkov told The Daily Beast, “Unfortunately, I believe that an escalation of the conflict and clashes between Russian- and Western-supported forces are possible.”

When the Russian independent radio station Echo of Moscow conducted a survey after Putin’s security council meeting asking whether the station’s listeners believed there could be a direct military conflict between Russia and the West, 43 percent of the audience said, “Yes.”

Here at Yavoriv, in the shade of a military vehicle, two veterans of wars in the Middle East, Zachary Savarie, 28, from New York state, and Allen Porter, 33, from Missouri, were discussing the challenges Ukrainian soldiers were facing in Donbas. What would they do if their units were surrounded with Russian-made tanks and Russian-backed forces? The traps and encirclements in which Ukrainian soldiers have suffered major losses have occurred at least twice in the past year, in Ilovaysk and in Debaltseve, battles known as closed “kettles” in Russian military parlance.

“Let me think for a moment, that is a difficult one,” said Porter, who served three tours in Iraq and two in Afghanistan. “Whenever you are surrounded, it’s a bad day,” he told The Daily Beast.

For the U.S. military, this is “a mission of high responsibility to train soldiers to fight for their country’s sovereignty,” Savarie said. Since April 2014, the Ukrainian military has lost more than 2,495 soldiers, killed by Russian-backed rebel forces. “We have never had such bad casualties in one year,” said Savarie, a veteran of two tours in Afghanistan up against the Taliban. “We rarely or never saw massive forces backing our enemy, we have not faced numerical superiority, so we can take lessons from Ukrainians, ask them how they apply skills in different situations.”

The U.S. military is drawing on its own experiences to teach the Ukrainians how best to survive under heavy artillery barrages, tank and sniper attacks, how to defend their positions with the resources they have, and many other useful skills, some of them excruciatingly obvious. (One basic lesson: Don’t kick what may be improvised explosive devices found on the ground.)

The Ukrainian soldiers are grateful, especially for the equipment the U.S. military has provided, including long-range radars, drones, and night vision equipment, Ukrainian National Guards officer Vadim Perepichka told The Daily Beast on Wednesday. “The most useful experience I had during my two months with the U.S. Army’s 173rd Airborne Brigade was the night program, when we learned to conduct special operations wearing night vision goggles,” Perepichka said as he headed back to the front lines.

The Organization for Security and Co-operation in Europe (OSCE), meanwhile, reported an escalation of the fighting outside Donetsk in eastern Ukraine. Kiev reported attacks by about 400 rebels supported by tanks in Starokhnativka village outside Mariupol, a strategic port on the Sea of Azov. Rebel leaders denied the attacks.

By the end of the program about 500 Ukrainian National Guards are to be trained by the U.S. military. British Defense Minister Michael Fallon also said Tuesday that British veterans of wars in Iraq and Afghanistan were planning to train more than 2,000 Ukrainian soldiers by the end of this year.

The soldier students of Yaroviv are not under the Ukrainian Defense Ministry’s regular army but from units of the National Guards, some professional, some volunteers or drafted soldiers without any proper military training. But their motivation is impressive, they are eager to learn new skills, and they ask every day for new challenges.

Beginning this week, U.S. paratroopers are preparing to teach their students to conduct squad maneuvers in live-fire exercises in order to proceed with Fearless Guardian, a military training program approved by the U.S. Congress and run by both the State Department and the Pentagon. The mission and the program of instruction come at the request of the Ukrainian government. The paratroopers are in Ukraine for the second of three rotations scheduled to last through November.

Moscow has complained frequently about the “provocative” presence of the U.S. paratroopers in Yavoriv, blaming Washington for threatening the peace. “With a smokescreen of claims about an alleged presence of Russian troops in Donbas, Washington is trying to divert the international community’s attention from its military deployment in Ukraine,” the Russian Foreign Ministry spokesman, Alexander Lukashevich, said in a statement last April. “It’s obvious that the U.S. troops on Ukrainian soil won’t bring it peace.”

By July the number of foreign military on Ukraine’s soil had increased to 1,800 soldiers. The exercises were organized by International Peacekeeping and Security Center in the Lviv region and focused on defensive operations as well as integrated command posts for units from 18 countries.

Once again Moscow was angry: “The military drills involving NATO members and Ukraine’s army that started in Lviv region under U.S. command are a clear demonstration of NATO’s provocative policy to unequivocally support the policies of the current Kiev authorities in eastern Ukraine,” the Foreign Ministry said in a statement.

Both for Ukrainian society and the professional military, it is important that the world has pulled together to support their country, Ukrainian Defense Ministry spokesman Oleksandr Poronyuk told The Daily Beast. “Russian leadership knows perfectly well that we have had joint military exercises with NATO for 20 years here outside Lviv. This is the biggest training field in Europe; it can be useful for any NATO member, and for our military it is important to develop from the army of the fifth generation, like the Russian army, to the army of the seventh generation, like they have in the U.S,” Poronyuk said.

During the Cold War, Colonel Poronyuk joined the Soviet military and for over a decade served in Russia without the slightest idea that one day his home city of Lviv would host U.S. paratroopers training Ukrainian soldiers.

For the U.S. military, the changes in relationships with Russia in the past few years are dramatic, as well. Only two years ago, in 2013, Porter was involved in bilateral military exercises with Russian airborne troops. “Just one year later, in 2014, I was based in Estonia waiting for Russia to attack, and this year we are here training to fight a Russian enemy,” he said.

“The enemy is not just one thing—they dress different, they look different—we need to be flexible, ready for anything, ready to go anywhere and do anything,” Savarie added.

And how does it strike you, after years fighting Iraqis and Afghans, that your enemy now is just as blue-eyed and blond as you? “We heard from the Ukrainian military that sometimes a brother has to fight against a brother in the east of their country. That just blows your mind,” Porter said.

There are many lessons to be learned on Ukraine’s battlefield—for all sides.