Since then, the Soviet Union has collapsed and Russia itself is disintegrating. A united Germany has become the most powerful country in Europe and America's closest ally. America itself still keeps forces in Europe but is increasingly conscious of its responsibilities as the world's only global super power. Its commitment to collective security in Europe through Nato is continually challenged in Congress by an odd alliance of isolationists and unilateralists.
In one sense, the end of the Cold War has made Nato a biological monstrosity - an organ without a function. When I asked a bright young officer from Brussels how many people are now working at Nato's HQ he replied: "About 20 per cent".
Yet Nato is as valuable as ever. It provides a political and security framework through which the United States can involve its forces in peacekeeping, or peace-making, not only in Central Europe but also in south-eastern Europe, the Mediterranean and the Middle East. The United Nations, which was set up to provide such a framework, has been rendered impotent by the veto of Russia and China.
In recent years Nato has made increasing efforts to develop co-operation with Russia in order to create a new framework for European security - an Organisation for Security and Co-operation in Europe.
However, by accepting Poland, the Czech Republic and Hungary as members, and by opening the prospect of membership to countries in the Baltic and Eastern Europe, Nato has dangerously undermined its relations with Russia, and strengthened Yeltsin's Communist and nationalist opponents. This process has been aggravated by Nato's decision to intervene in the civil war in Yugoslavia without consulting Moscow.
The bombing of Serbia was particularly offensive to Russia since it took place when Prime Minister Yevgeni Primakov was in fact half-way across the Atlantic for talks in Washington; even liberals such as Yegor Gaidar were appalled. The bombing was against the advice of the US military and was most unwelcome to Yugoslavia's neighbours in Nato, Greece, Italy, and Hungary - which has a large minority in northern Yugoslavia.
Even the Secretary General of Nato has expressed disquiet that there was no serious prior discussion with Nato on the operation's aims or means. It is still unclear whether Nato would be involved in providing land forces in Yugoslavia - and for what purpose.
All observers agree that the bombing has strengthened Milosevic's political position in Yugoslavia and has led to more savage attacks on the people of Kosovo. Moreover, it has led to the death of innocent civilians in Belgrade and elsewhere - notably on a road convoy of Kosovar Albanian refugees this week.
There is growing disagreement in Washington over the operation's aims and targets; above all, there is no apparent exit strategy.
The best and now the only hope is that Nato may accept the need to engage with Russia in a major attempt to get a peaceful settlement of the Kosovo crisis, even if that means significant changes in Nato's present policy.
However, Nato's forthcoming summit meeting on 23 April may create new difficulties. It may publish a Membership Action Plan for Bulgaria, Romania, Slovakia, Macedonia, Albania and Slovenia, which will be offered earlier membership provided that they modernise their entire armed forces in line with Nato - thus giving them priority over the Baltic States and former Soviet republics.
Moreover, it will open the possibility for Nato action beyond the existing treaty area, including central Asia. Nato has already carried out military exercises in Kazakhstan under American leadership. Nato is also requiring such countries to prepare more actively for participation in some type of a rapid reaction force.
America also wants the Summit to adopt a strategic concept that will include a new commitment to protect common interests and to act jointly against the proliferation of weapons of mass destruction.
President Clinton has said that tomorrow's alliance must defend us against threats to our collective security from beyond Nato's borders, including the spread of weapons of mass destruction, ethnic violence, and regional conflict.
In theory this could open the way to Nato intervention in the Middle East and in North Africa. This has alarmed some Nato leaders in Europe.
The French Parliamentary Defence Committee has gone much further. In its recent report it declared that last year's American missile strikes on Afghanistan and the Sudan show that Washington was "thumbing its nose at international organisations".
It also made it clear that France would not join any American-led effort to deploy an anti-missile shield in Europe, saying that "it could give the impression that Nato, having lost its enemy to the East, is now looking for one in the South".
Moreover, it added, "installing Nato a few dozen kilometres from St Petersburg could seriously damage relations with Russia".
In stressing the need for a strong European identity within Nato, the French report argued that this would allow Europe to mount peace- keeping missions alone, if Washington proved reluctant to act.
It is clear that Tony Blair's idea of a European identity on foreign and defence policy may be interpreted differently across the Channel.
Once again Britain's determination to put first its relations with the United States is creating serious problems for its desire to appear at the heart of Europe.
It is high time that Britain used its position in Nato to seek changes in American policy - particularly with regard to Yugoslavia.