After a series of meetings on neutral territory US President George Bush and his Russian counterpart, Vladimir Putin, get together this week for their first real summit.
Mr Bush will be following in the footsteps of previous American presidents, who hosted Russian and Soviet leaders.
But this time there is one big difference - discussions will be held in an atmosphere of cooperation, not confrontation.
Frosty start
At the start of 2001, the idea of the two leaders meeting in such a warm spirit seemed highly unlikely.
Mr Putin, who became his country's head a few months before Mr Bush stepped into the White House, was decidedly cool about relations with the US.
A couple of alleged spy scandals in Russia gave the impression that Mr Putin would not be unduly concerned if relations became chilly once more.
Mr Bush also did not go out of his way to extend the hand of friendship to Moscow.
His emissaries were letting it be known around the world that the new American president planned to treat Russia as simply "any other country".
War on terrorism
This began to change after their first meeting in June.
A great deal of useful work in improving relations was done also by the US Secretary of State, Colin Powell, and the Russian Foreign Minister, Igor Ivanov.
Then, when planes were hijacked and flown into the World Trade Centre and the Pentagon on 11 September, Russia and the US were thrown closer together than ever before.
Mr Putin was the first foreign leader to telephone Mr Bush to offer his nation's condolences over the tragedy.
And he soon made it clear that he was putting Russia's resources - apart from troops - at the Americans' disposal.
The war on terrorism is now the dominating feature of the US-Russian relationship.
Star wars
Matters such as US threats to tear up the Anti-Ballistic Missile Treaty by creating a National Missile Defence Shield have suddenly taken a back seat.
But that does not mean that the question of the NMD has disappeared from the agenda altogether.
On the contrary, it is expected to feature highly in this week's discussions.
Neither man wants to spoil the mood of cooperation by maintaining the kind of intransigent positions which looked likely to spoil the relationship before 11 September.
Mr Putin, though, has gently tried to point out to Mr Bush that what happened then shows that the threat to America's security is one which can not be solved by a missile shield.
Russia maintains that the ABM Treaty has helped keep the peace since it was signed in 1972.
The idea is that if either of the superpowers of those times - the USA and the USSR - had created an effective defence against the other's nuclear missiles, they would have been more likely to use nuclear weapons themselves, believing that they could survive a nuclear first strike.
It looks likely that a compromise will be reached. The Americans may be allowed to conduct limited missile tests, as long as they do not abrogate the treaty completely.
Nuclear worries
If Mr Putin were to soften his opposition on this, it would encourage Washington to look more favourably on Russia's bid to join the World Trade Organisation.
This has already been boosted by the state of the Russian economy.
Russia has had two years of economic growth, albeit helped by oil prices which were high for a time.
But even if oil prices fall further, a friendly Russia could be seen by the West as a reliable supplier of oil.
Russia is already the world's second largest oil exporter.
And the state of the Russian economy means that Mr Putin is not coming to Washington with a begging bowl.
One big concern still stands in the way of a further improvement of US-Russian relations.
Osama bin Laden's claim last week that he is in possession of a nuclear weapon may have been dismissed by the West as a bluff.
But the Russians themselves admit that the security of their nuclear facilities is far from perfect.
Mr Bush will want to know from Mr Putin what is being done to improve the situation.
Yet Mr Bush might offer US help to solve what is ultimately another facet of the joint struggle against terrorism.