Country reports: UK Foreign and Commonwealth Office and US State Department.
The BBC World Service programme The Works has been to Russia to assess the situation there.
Russia faces potentially severe problems from the millennium bug. Despite having fewer computers than other leading nations, it is generally ranked in the bottom category in dealing with the Y2K problem.
The US State Department reported in September that disruptions wre likely to occur in "the key sectors of electrical power, heat, telecommunications, transportation, and financial and emergency services".
On 12 July, Alexander Ivanov, head of the State Communications Committee, announced that only one third of the country's 28,000 vital computer systems were ready for Y2K.
He said the Russian Central Bank and most fuel and energy companies were prepared, but the number of flights would be reduced and some dangerous industrial processes halted for safety reasons.
Another senior official estimated that 400 of the countries 600 airports would experience Y2k difficulties.
A question of cash
Russia did not really begin taking steps until May 1998 and is desperately short of cash. Estimates of how much the government needs vary wildly, from an initial $500m, to $3bn but then back down to $187m on 12 July.
The higher figure represents 15% of the annual federal budget and a figure which the precariously financed government simply does not have.
The lack of cash led the Duma to order government and private bodies to develop plans to avoid chaos, but at their own expense.
Although there are concerns across the board, there are two areas of particular concern for the rest of the world - Russian nuclear missiles and Russian nuclear power plants.
When the screens go blank
The missiles themselves are not thought to be a major risk in practice. After the purchase of new hardware and reprogramming, launch and warhead control systems have been declared Y2K safe.
Early warning systems are more of a problem and US military experts have been working with their Russian counterparts to avoid major problems. The fear is that the screens could go blank or even give false readings of a nuclear strike - prompting a counter-strike.
Cost is again a factor, however, with the Russian military saying it has only $4m to spend on Y2K. However, the US and Russia have finally set up a centre to watch for any false alarms caused by the bug - the original proposal was delayed during tension over Kosovo.
Power station worries
As late as June 1998, a nuclear industry spokesman was declaring that he and his colleagues would wait until the year 2000 itself before trying to tackle any problems.
These would probably hit control systems, temperature and radiation monitoring and automated emergency-response procedures. Although Chernobyl is in the Ukraine, there are worries that the 1986 incident could be repeated if too many systems fail at the same time.
One mitigating factor is that former Soviet nuclear reactors are less dependent on computers, with analog devices controlling most critical systems such as water cooling pumps. Another is that the system has plenty of spare capacity, so if individual power stations go down it should not cause national problems.
In March, the Russian Atomic Energy Ministry said 97% of date-sensitive components had been checked and that all those which dealt with reactor operations or radiation containment had been declared safe.
The Ukraine is another area of international concern. It has 14 reactors including some still online at the Chernobyl site.
However, nuclear industry head Olexander Parkhomenko stated in March that most of them were too outdated to suffer from the millennium bug.