Steve Bates, head of emerging markets at Flemings, points out: "These areas are very volatile and the funds go up and down a great deal. But if you have a strong tolerance for risk it can be very profitable".
The Eastern European markets have had a good year so far. The Czech Republic stock market is 16 per cent higher than it was 12 months ago, the Hungarian market is up 110 per cent, the Polish market is up 61 per cent and the Russian market is up 116 per cent. This compares with a 19 per cent rise in the US S&P share index over the last year, and the FT World Index's rise of 10 per cent.
But it has not been a smooth ride. In fact, since the end of September, the Czech Republic stock market has fallen 11 per cent and the Polish market is down 6 per cent, while the Russian market is up 14 per cent.
This volatility means that people should never be a position where they may need to realise their investment at short notice, says Rory Landman, a fund manager at Baring Asset Management. "Investments in these markets are for grandchildren, not widows and orphans," he says.
But the overall story has been positive. These markets, still seen as underpriced, are expected to continue to grow over the long term. "The performance this year is based on solid foundations, because the markets started off so cheap," says Mr Landman.
But Eastern Europe is by no means homogeneous. The Central European countries, such as Hungary, Poland and the Czech Republic, are experiencing strong growth, have got inflation under control and are politically more stable. These countries are catching up with Western Europe and are on course to join the European Union.
Russia started its recovery later, and is forecast to achieve economic growth for the first time in 1997. Russia also is different in that it does not look likely to join the EU in the near future. But its attraction for investment is that it is a major economic power in its own right.
There is a whole range of offshore funds investing in Eastern Europe, many based in Luxembourg. Those offering funds include Barings, Schroders, Flemings, Foreign & Colonial and Mercury Asset Management. Some of them invest in only one Eastern European country; these typically are based offshore and are more volatile than those which spread the risk over several countries.
Some countries, such as Poland, go out of their way to attract foreign investors with tax incentives, says Isabel Knight, fund manager of Foreign & Colonial. "Poland is one of the most attractive areas," she says. "It has a stable economy and is well regulated."
A number of unit trusts and investment trusts also invest in Eastern Europe. Some invest in other emerging markets as well, such as Latin America.
For more information, interested investors should speak to an independent financial adviser or a private client stockbroker. Often it is possible to invest in funds only through one of these channels