The US top shares index, the Dow Jones, has surged by nearly 500 points or 6.5% - its biggest one day gain in almost 15 years.
And preliminary figures suggest that the US stock markets had their busiest ever day of trading.
The strong rise of US share prices dragged European indexes higher at the end of their trading day, and sparked renewed hopes of a market recovery.
The market's sudden strength came after action by the US Congress to crack down on the corporate fraud that has undermined investor confidence recently.
Lawmakers agreed reforms that will regulate America's accounting profession and increase penalties for business executives convicted of fraud.
But after the markets closed, the US stock market regulator announced that it was investigating the accounting practices of media giant AOL Time Warner as well as 12 investment firms over the conduct of their securities analysts.
The latest investigations may dent confidence that the worst of the stock markets' troubles are over.
And all eyes will be fixed on Thursday's open to see whether the rally can be sustained.
Europe recovers
Germany's Dax, which had lost more than 6% earlier in the day, had dragged itself back into positive territory by late afternoon trade, before closing 3.3% higher.
But the US rally came too late to save France's Cac and the UK's FTSE from finishing up in the red.
The FTSE, which had been over 200 points lower during the day, closed 81 lower at 3,777.
"People are jumping to get in because they don't want to miss the bottom," fund manager George Mairs told Bloomberg News.
"No one is prepared to say the bear market has ended, but the magnitude of this rally is very impressive.''
Misguided optimism?
But other analysts still fear that the markets have further to fall.
"We're still dealing with terrorism, accounting issues and fundamentals, which appear to be showing signs of further deterioration," said Matthew Johnson, managing director of trading at Lehman Brothers.
The US government has been trying to restore confidence in the economy's growing strength.
"When you take a look at the data, the hard, cold facts about the economy, it is growing solidly," said White House spokesman Ari Fleischer.
Rumbled
Analysts attribute the change in direction to the arrest of top Adelphia Communications executives, demonstrating a tough new stance on corporate ethics.
And US lawmakers agreed on new legislation aimed at tightening the regulation facing companies.
Investor confidence had been knocked for six on Tuesday, after accusations that two of the world's biggest banking groups had helped Enron disguise the scale of its debts.
Last week's worldwide stock market falls have been the culmination of a two-month slump that has wiped up to one-quarter of the value off the world's top companies.
The bear market - the broker's name for a sharp and long-lasting drop in share prices - is now in its ninth week, with the Dow Jones index well below its post-11 September trough.
(China Daily July 25, 2002)
