* Russia-NATO ties strained by expulsions, exercises
* Russia, NATO are testing each other's resolve - analysts
* Strains in relations could affect U.S-Russia ties
BRUSSELS, May 6 (Reuters) - The real conflict as NATO holds military exercises in Georgia is an increasingly tense battle of wills between the Western defence alliance and Moscow that could affect efforts to improve U.S.-Russian relations.
Ties between the former Cold war foes have soured over the exercises and an espionage case in which NATO has expelled two Russians and Moscow has thrown out two alliance officials. Russia has also pulled out of a meeting scheduled with NATO.
NATO says broadening ties with former Soviet republics such as Georgia, with whom Russia fought a brief war last year, breaks down barriers with countries long dominated by Moscow and strengthens security and stability in Europe.
But Russia regards such moves as a security challenge and wants to roll back Western influence in areas it considers part of its traditional sphere of influence.
"What you are seeing here is some power play, arm wrestling and arm twisting," said Karl-Heinz Kamp, research director at the NATO Defence College in Rome which prepares personnel for alliance appointments.
Diplomats and analysts say each side is testing the other's resolve over how to have influence in Ukraine and Georgia, which have been promised eventual membership of NATO.
This is part of a larger battle of wills as President Barack Obama tries to improve U.S. relations with Russia which deteriorated sharply under President George W. Bush.
U.S. officials say signals coming from Moscow are uneven and it is unclear how far Russia wants to go in improving ties.
"Russia is trying to stop the enlargement of NATO and roll back Western influence in eastern Europe," said Tomas Valasek, of the Centre for European Reform think tank in London.
"They have been testing to see how much it (the West) is willing to concede...but at no point has the Obama administration suggested they are willing to sell out eastern Europe."
Russia put a lot of pressure on NATO to cancel the month-long military manoeuvres which began in Georgia on Wednesday, with more than 1,000 soldiers involved in crisis response and peacekeeper training exercises.
It has described the exercises on its southern flank as "muscle-flexing" after the war in Georgia last August, when Russia crushed a Georgian military attempt to retake the pro-Moscow separatist region of South Ossetia.
NATO has dismissed the criticism, saying Moscow knew about the exercises long ago, but some defence analysts are critical of its decision to press on with the war games.
"Given there was a conflict in the region last August you can say the decision on the exercise was a risk, and in many ways there is still the possibility of conflict renewing," said Andrew Monaghan, Russia expert at the NATO Defence College.
He said NATO had sent contradictory signals to Moscow over Georgia, avoiding direct involvement in the conflict last year but then pressing ahead with the military exercises.
"VOLCANO" OF NATO-RUSSIA TIES
The row has set back efforts to improve NATO-Russia after the resumption of formal contacts last week, eight months after they were suspended because of the war in Georgia.
Foreign Minister Sergei Lavrov on Tuesday pulled out of talks with NATO. The tit-for-tat expulsions over a spying case involving sensitive documents obtained by Russia's SVR foreign intelligence service have also not helped the atmosphere.
"It is as if we were scientists studying the workings of a volcano," Russia's NATO envoy, Dmitry Rogozin, said of the NATO-Russia relationship. "It proves it is a very unpredictable natural phenomenon and we can expect an eruption at any time".
He said the expulsions of two Russian diplomats from NATO headquarters had been driven by elements in the alliance who wanted to undermine Western ties with Russia.
It is not clear how much each side is ready to risk in the disputes. Each has an interest in smooth relations, especially as NATO seeks Russian cooperation in the war in Afghanistan and the West seeks Moscow's help over Iran's nuclear programme.
But NATO's resolve has hardened since last year, when countries such as France and Germany opposed putting Georgia and Ukraine firmly on the path to membership and they won only a vague promise of eventual membership.
Monaghan said there was clear agreement on both sides of the Atlantic that Russia's belief in its right to spheres of influence was unacceptable.
"Now there seems to be greater consensus within the alliance to continue to conduct exercises in what's clearly an unstable area. It's probably not very fortunate and I don't think it will add a great deal to the stability of the region," he said.
"I think we are in for a difficult couple of months."
Our Standards: The Thomson Reuters Trust Principles.