The most important is a report, published by Russia's foreign intelligence service, that all but warns the West not to interfere with Moscow's plans to reintegrate most former Soviet republics into a new union. Another signal is Russia's refusal to recognise a pounds 5bn oil-field development deal signed by Azerbaijan and a Western consortium.
However, these prickly issues may well be played down during Mr Yeltsin's visit. According to the Foreign Office, one highlight of his trip will be a tree-planting ceremony at Chequers tomorrow.
Mr Yeltsin and John Major have one over-riding reason to keep up a positive atmosphere during their talks. This is the fact that Britain and Russia are closely co-ordinating their policies on the Bosnian war and agree that the United Nations Security Council should not lift its arms embargo on the Muslim-led Bosnian government.
The Clinton administration has pledged to ask the Security Council to lift the embargo after 15 October if the Bosnian Serbs do not accept a Western-Russian initiative to split Bosnia into a Bosnian Serb territory and a Muslim-Croat federation. Britain and Russia fear that lifting the embargo would lead to a wider war in the Balkans.
Despite its reservations about Nato's role in Bosnia, Russia has gradually lost patience with the Bosnian Serbs because of their refusal to endorse the international peace plan. Andrei Kozyrev, the Foreign Minister, yesterday supported Nato's air strike on Bosnian Serb forces on Thursday, saying: 'The Muslims are resorting to provocative acts, to attacks, but the Bosnian Serbs, as always, are reacting inappropriately, overdoing it substantially.'
Although Britain and Russia see more or less eye-to-eye on Bosnia, London and its Western allies are rather more concerned about Moscow's policies in its former Communist sphere of control. The 11 former Soviet republics that are grouped with Russia in the Commonwealth of Independent States (CIS) are nominally sovereign countries, but in practice Russia is wielding more and more influence over the region.
Nato and neutral countries complained this month that Russia had arranged an Armenian-Azerbaijani summit in Moscow without informing the Conference on Security and Co-operation in Europe (CSCE) and had pressed for a Russian-led CIS peace-keeping force to be deployed in the war zone of Nagorny Karabakh rather than a CSCE-sponsored force. Western officials pointed out that Russia's unilateral actions were inconsistent with its professed belief that the CSCE should be the supreme international security organisation for Europe.
Another problem concerns Moldova, where there are signs that Russia is backtracking from an agreement, reached in principle last month, to withdraw its 14th Army. The army has played an important role in propping up a Communist-led separatist state in eastern Moldova, known as the Dnestr Republic.
Perhaps the most sensitive case is Russia's relationship with Ukraine, dogged by disputes over nuclear disarmament, energy supplies, ownership of the Crimean peninsula and the status of the Black Sea fleet. Russia's Black Sea fleet commander, Admiral Eduard Baltin, alarmed Ukrainians this week by calling for 'an economic, political and military drawing together of the two Slavic states'.
While the West may tacitly accept Russia's predominance in the former Soviet area, with the important exception of the three Baltic states, there is more at stake for both sides in central and eastern Europe. Russia is still determined not to let Nato expand eastwards and include the Czech Republic, Hungary, Poland and Slovakia.
Mr Yeltsin's central theme is that the West must not seek to minimise Russia's international role or treat Moscow as a junior partner whose assent to Western policies is taken for granted. 'Russia is playing a pivotal role in world changes, and its voice is becoming weighty, innovative and timely. We are now not merely listening to what people have to say, but are ever more actively formulating proposals, terms and demands,' he said recently.