According to some Nato officials, Russia's Foreign Minister, Yevgeny Primakov, indicated to alliance leaders in Berlin on Tuesday that the Kremlin would not resist Nato's expansion provided that nuclear weapons and Western military bases and troops were not brought into new member states. Such states would, however, enjoy the full collective security guarantee that comes with Nato membership.
Publicly, Nato says there is no deal with Russia and that the terms of membership are a matter exclusively for Nato's 16 national governments and the candidate countries. However, Nato officials acknowledge that it is unrealistic to address such an important security issue without taking Russian concerns into account.
Although Nato is reluctant to name the countries that will be admitted first, there appears to be a tacit understanding with Russia that they will be the Czech Republic, Hungary, Poland and possibly Slovakia. This is because, broadly speaking, they lie some distance from Russia's frontiers and are seen as successful young democracies with strong Western historical and cultural traditions.
Poland shares a border with the Russian enclave of Kaliningrad, but the danger of a Nato-Russian confrontation in this area would be reduced if there were an understanding not to base Nato armies in Poland. A question mark hangs over Slovakia's entry into Nato because the US and European Union are dissatisfied with the quality of Slovak democracy.
Even if Moscow has accepted that the Czechs, Hungarians and Poles will join Nato, the Russians are unlikely to let the alliance get off scot- free. For one thing, Nato's expansion would render redundant the 1990 Conventional Forces in Europe (CFE) treaty, which was based on European military and political arrangements that would no longer exist.
Nato recognises the need for some changes to the CFE treaty, but if it lapsed altogether Russia could see a chance to rearm and redouble its efforts at turning the Commonwealth of Independent States (CIS), made of up all former Soviet republics except the Baltic states, into a military alliance. Russia might also refuse to ratify the Start-2 treaty on reducing intercontinental nuclear weapons.
According to Russian defence sources, Nato's enlargement could cause Russia to target new member states with tactical nuclear weapons. One Polish scenario anticipates extra Russian forces in neighbouring Belarus and nuclear weapons on Russian submarines in the Baltic Sea.
Even a cautious Nato expansion into central Europe is unlikely therefore to be trouble-free. But much greater problems could arise for countries excluded from the first stage of enlargement, especially Estonia, Latvia and Lithuania.
This was made clear in a report by the Moscow-based Council on Foreign and Defence Policy, an independent institute with broadly liberal or centrist political views. Even these moderate Russians warned that Nato enlargement into central Europe "implies turning the Baltic states and possibly Ukraine into a zone of bitter strategic rivalry".
Although committed to the Baltic states' independence many Western governments privately regard the three countries as unsuitable candidates for Nato. Despite their desperation to join, they are seen as so small and close to Russia that they are virtually impossible to defend. Estonia and Latvia have difficult relations with Russia, partly because both contain large ethnic Russian minorities.
Yet Western states, especially the Nordic countries, do not wish Moscow to gain the impression that Nato is indifferent to the fate of the Baltic states.
However, the inescapable fact is that such steps would not give the Baltic states the collective security guarantee that is the most precious element of Nato membership. As for Ukraine, Nato's expansion up to its borders would put it under Russian pressure to join a common CIS defence, something the Ukrainians are keen to avoid.
Limited Nato enlargement may pose problems for Bulgaria and Romania. Russia views that part of the Balkans as an area of traditional influence, and President Boris Yeltsin recently outraged Bulgarians by suggesting their country might like to join the CIS.