The Dow Jones industrial average was 57.22 points higher at 7,555.54 in the first minutes of trading.
Wall Street got some reassurance that its record gain of the day before might hold up when Hong Kong investors sent the main index there up nearly 19 percent. The rally spread to Tokyo, which rose 3.3 percent, and London, where the main index was up 2.1 percent by midafternoon.
Also today, Federal Reserve Chairman Alan Greenspan said the market decline could have a beneficial effect in the long run.
On Tuesday, the Dow soared 337 points in its biggest one-day gain ever, erasing more than half the previous day's record drop of 554 points.
Trading slowed considerably from Tuesday's blistering pace, which produced the heaviest volume in Wall Street history despite some technology glitches that delayed many investors' orders.
Overall, more than 2.8 billion shares changed hands on U.S. markets Tuesday thanks to a crush of investors eager to make deals after trading was halted abruptly by Monday's selloff. The Nasdaq Stock Market became so bogged down that it was unable to calculate its composite index for more than 90 minutes after the close of trading.
The huge volume slowed online trading, leaving many would-be buyers watching the market's rapid climb while they tried fruitlessly to get their orders in. E-Trade said it faced a huge backlog of demand that had the company scrambling to catch up. At Fidelity Investments, the world's largest mutual fund company, some trades also were delayed because of an increase in visitors to its Web site.
As stock prices quickly escalated Tuesday morning, a delay of just a few minutes meant paying more for shares. IBM shares, for example, rose $10 in a half-hour span.
E-Trade processed 50,000 trades Tuesday, more than double its average daily volume of 24,000 in the third quarter.
The Dow Jones industrial average opened Tuesday with a 178-point drop, then surged an unprecedented 337.14 to 7,498.32. More than 1 billion shares were traded on the New York Stock Exchange and the Nasdaq, both records, and nearly 3 billion shares changed hands on all U.S. markets.
IBM's early announcement that it would buy back up to $3.5 billion worth of its stock was seen as a turning point. Companies buy back their stock to tighten the supply of shares, boosting their value and making them attractive to buyers.
As the stock of International Business Machines went higher, so did share prices of other big companies hammered by worries that economic turmoil in Southeast Asia would hurt their profits.
IBM's announcement also boosted the battered technology sector, which was seen as particularly vulnerable to Asian troubles. The technology-heavy Nasdaq composite index surged a record 67.93 points to 1,603.02, a gain of 4.3 percent.
"Investors have learned to buy on the dips. As soon as they saw a stabilization of the market, the money came pouring in," said John Eade, director of research at Argus Research in New York.
But Eade and other analysts warned that more turbulence could lay ahead.
"I don't think we have reached the depth of the turmoil in the Pacific Rim countries," he said.
While Monday's record point loss ranked as the 12th worst in percentage terms, the 4.71 percent day-after rally by the Dow was only the 70th biggest.
Still, analysts said it showed the United States has one of the world's most stable economies.
"When cooler heads prevail, the U.S. economy looks far more solid than the Far East," said Jim Weiss of State Street Research and Management in Boston.
And there was good news for individual investors, who were given some credit for showing persistence throughout the recent rout.
The stock market's volatility helped the bond market, leaving long-term interest rates at 20-month lows. That makes it cheaper to buy a house or borrow money to build a factory.
Investors also were given a chance to use the buy-on-the-dip strategy that served them well in the 1987 crash and subsequent downturns in an otherwise smooth upward market.
"I'm not selling anything right now," said Peggy Schmeltz, 70, of Bowling Green, Ohio. "In fact, I'm looking to eventually buy."