Russian and American negotiators began work at the weekend on their ambitious plans to rid the world of nuclear weapons. The talks are intended to produce a new agreement to replace the 1991 Strategic Arms Reduction Treaty (Start) that expires in December. This time, however, both sides are committed to cutting their arsenals well below the current combined total of 5,000 warheads, after the declaration by presidents Obama and Medvedev in London on April 1 that they would work towards the scrapping of all nuclear arms. It is a fraught endeavour, but a very worthwhile one.

It is a visionary aim, and revives one of the main vehicles for reducing East-West tensions during the Cold War. President Obama has returned to arms control, one of the goals outlined in his inaugural address, as a way of improving America's strained relations with Russia. But it will be difficult to achieve. For as warhead numbers are reduced, related issues become more complicated. If, for example, both sides cut their totals to 1,500 each, verification becomes more important, especially for the Russians, who know that the Americans could rebuild their arsenals more quickly. And this would mean Russia's defence ministry and arms factories accepting more transparency than they have before.

The second issue is delivery systems. Russia fears it will lose out in cuts, as its long-range missiles are ageing and probably far less reliable than US missiles. Last week Mr Medvedev insisted that any new treaty should limit all systems, including the strategic triad of intercontinental ballistic missiles, submarine-based missiles and heavy bombers. But the Americans have an advantage that strategists might be reluctant to abandon, especially as they are deeply worried about the threat of missiles fired by states still building up offensive capabilities. But with warhead numbers reduced to about the 1,000 mark proposed by Mr Obama, the US would have to consider abandoning one leg of its strategic triad.

The third risk in a drastic reduction of warheads is that the two former superpowers have less of an advantage over other nuclear powers, especially China. The deterrents still hosted by Britain and France are unlikely to upset the balance, but China appears determined still to maintain its arsenals at current levels, as do India, Pakistan and Israel. The importance, therefore, of each warhead being up to date and fully operational increases. That will make it harder for Mr Obama to persuade Congress to ratify the Comprehensive Test Ban Treaty, which it refused to do in 1999. It may also raise pressure to resume some form of testing.

The talks will also raise questions about other arms treaties. The Russians are unwilling to make concessions as long as the US is committed to the Bush Administration programme of installing an anti-missile shield in Poland and the Czech Republic. Mr Obama has signalled that this may not now go ahead, but much depends on Iran and North Korea, which have reacted aggressively to his conciliatory overtures.

The key issue in all talks will be mutual trust. That broke down during the Bush Administration. The relationship may now be on the mend. But it will take months of tough bargaining before either Russia or America is ready to lead the way to a world without nuclear weapons.