Top brass from both sides will watch missile warning screens side by side in a specially constructed building until a week after the new year. They will try to detect false alarms from computer glitches, and avoid launching nuclear strikes in response.
But leading experts - including Nobel Peace Prize-winners and one of America's most distinguished bomb designers - says this does not go far enough, and are campaigning for Presidents Yeltsin and Clinton to deactivate their nuclear arsenals over the turn of the year. They say that the dangers have been made even greater by the tensions over the war in Chechnya.
The two superpowers have 4,400 nuclear weapons - more than enough to destroy the world - ready to be launched at a moment's notice. In the past, experts say, false alarms generated by faulty equipment have caused an alarming number of near misses: on one occasion a poorly designed chip, costing just 64 cents, deep in the US Defence Department's telephone switchboard hardware, started sending out signals that a Soviet attack was under way.
Last year an authoritative report concluded that there could be "no confidence" that the Pentagon would get its systems ready for Y2K, as the millennium bug is known in the US. Though the US has enormously improved its preparedness since, experts say that no one can be certain that its systems are 100 per cent fool-proof; and there is acute alarm about Russia's decaying nuclear control system.
This Wednesday some 20 senior Russian officers will join a similar number of Americans at a specially built "Centre for Y2K Stability" in Colorado Springs near the US early warning command centre deep in the mountains.
The centre will become fully operational on December 28 and from then until January 7 two Russian officers and two Americans will sit side by side around the clock, with hotlines to their respective command centres.
The arrangement, which has echoes of the admission of a Russian general to the US war room in the film Dr Strangelove, is modelled on the shared system of air traffic control used in Berlin during the Cold War.
But experts insist that the chances of an accidental war remain. Sir Joseph Rotblat, a member of the war-time Manhattan project, who won the Nobel Peace Prize in 1995 for his work on nuclear disarmament, told The Independent on Sunday: "You cannot exclude the possibility that something may go wrong. The probability of it may be very slight, but the consequences would be enormous."
Professor Ted Taylor, who was one of the US's most senior bomb designers, adds: "No one can estimate the risk. It may be one in 10 or one in 1,000, but it is certainly there."
He says that keeping nuclear weapons on red alert after the end of the Cold War "may be one of the biggest mistakes humans have ever made".
Both have joined the campaign led by Dr Helen Caldicott, the founding president of Physicians for Social Responsibility, which is trying to persuade the leaders of both superpowers to deactivate their weapons.
The critics say that the danger is not that nuclear weapons will launch themselves automatically, but that the millennium bug will cause false alarms and shorten the 15 minutes in which a decision has to be taken on whether to launch a retaliatory strike. With tensions between Russia and the United States at their highest for years, even the joint control centre may not overcome the mistrust, they say.