Nato and Russian leaders are pledging to make a fresh start in their long, antagonistic relationship when they meet at a summit on Saturday in the Portuguese capital, Lisbon.
"We will leave behind us not only the Cold War, but also the post Cold War period... and will move forward," said Nato Secretary General Anders Fogh Rasmussen in a BBC interview.
In a video blog posted on the internet this week, Mr Rasmussen said he thought Russia shared his view that it was time to start working together.
Russian President Dmitry Medvedev will attend the meeting, making it the highest-level contact between the two sides since the crisis sparked by the war between Russia and Georgia in August 2008.
The conflict broke out just a few months after Nato had agreed with Georgia that it could eventually become a member state.
The decision infuriated Moscow, which still has a deep fear of being encircled by Nato. Ever since the collapse of the Soviet Union in 1991, it has watched helplessly as more and more Eastern European countries have joined the Western military alliance.
Afghanistan - a common concern
Now, echoing the positive noises coming from Nato headquarters in Brussels about the Lisbon summit, Russia's foreign minister Sergei Lavrov is talking about ending the era of "mistrust".
Underlying the calls for a new era of co-operation is a growing list of mutual interests. And at the top of that list is Afghanistan.
Moscow is just as concerned as Nato to see the Taliban quelled and Afghanistan stabilised so the country cannot be used as a base for Islamist militant groups.
Since the mid-1990s the influence of such groups has spread through Central Asia and into southern Russia.
It also wants to stem the flow of opium pouring out of Afghanistan - much of which has ended up in Russia, causing an epidemic of heroin addiction.
To that end, Moscow is training members of the Afghan police force.
Last month it also announced that its agents had taken part in a major drugs raid with US and Afghan forces, which destroyed heroin laboratories near Jalalabad.
At the Lisbon summit, President Medvedev is expected to agree to increase the overall level of assistance to Afghanistan, and not only to help tackle the illegal drug trade.
There have also been negotiations in recent weeks about expanding military supply routes running through Russian territory to Nato bases in Afghanistan, which were set up last year after Moscow and Washington pledged to "reset" their relations.
"Today we can transit goods (on trains through Russia) to Afghanistan," said Nato Secretary-General Anders Fogh Rasmussen.
"But it would of course be much more efficient if we could also take goods (on the trains) out of Afghanistan.
"We may also consider the list of goods which can be transported… but at this stage we cannot go into details."
The Russian supply route has become vital for Nato as military convoys travelling along the alternative route through Pakistan have increasingly come under attack.
Nato also wants Russia to provide the Afghan armed forces with helicopters, which are currently in short supply.
"One of the safest ways to get round Afghanistan is by helicopter," says Kurt Volker, a former US ambassador to Nato.
"And the Russians have a big capacity for this."
Moscow has offered to supply at least 20 helicopter gunships and train the Afghan pilots, but the deal has been delayed by Russia's insistence that it be paid for most of the aircraft.
But this is not the only price Moscow is demanding for its co-operation on Afghanistan.
"Russia is trying to make a trade-off... Afghanistan is where Nato needs Russia," says Dmitry Suslov, a military expert from the Council on Foreign and Defence Policy in Moscow.
"In return, Russia wants there to be no discussion of (further) Nato expansion to the countries of the former Soviet Union. Secondly, that Nato support some of Russia's interests in the European security field - such as limiting the expansion of US military infrastructure into Eastern Europe, and limiting the deployment of a US or Nato missile defence system in Eastern Europe."
It is a long list, and will test the limits of the current thaw in relations between the two sides.
Russia's ambassador to Nato, Dmitry Rogozin, has described the negotiations on missile defence as "uneasy and sticky".
"The problem is that even Nato members remain at odds on what this system must be like, what its timeframe is, and how much funding is needed," he says.
The Lisbon summit could well be an important step forward in the relationship between Russia and Nato.
But tough negotiations lie ahead before the two former foes can start co-operating on a broader range of global security issues.