Shares in the biggest banks gained smartly in heavy trading Tuesday as investors scrambled to buy stock in companies that had been punished in the recent market swoon.

Nearly every bank posted gains, and the Standard & Poor's bank index rose 2.34%, after a 2.26% rise Monday.

The Dow Jones industrial average also extended its rally, rising 139.80 points, to 8,714.65. And the Nasdaq composite index rose 2.04% on expectations that leading technology companies would post solid earnings.

The market got a further boost when, as expected, the Federal Reserve announced it had declined to raise interest rates.

But traders said the market's performance the past two days does not mean that investor jitters have subsided completely.

They said institutional investors are returning to stocks in big companies, the very same ones they were aggressively selling a few weeks ago, but are shunning the less liquid stocks of smaller companies. That suggests investor confidence has not yet swept the broader market.

Still, strategists said the market's gains so far this week indicate the worst of the summer selloff appears to be over.

They said the assorted economic and political ills-disappointing earnings, worries about Asia, concerns about the lingering investigation of President Clinton-that had combined to drive the market down 10% appear to be receding.

"The market was ripe for a correction," said Elizabeth J. Mackay, market strategist at Bear, Stearns & Co. "But the public didn't panic, and now mutual fund managers that have been sitting on all this money are putting it to work. And if there's a rally, there's a scramble to be a part of it."

But underneath the rally's gaudy numbers, some traders said they see the same weaknesses that plagued the market virtually all year.

"The top 100 names that got beat up recently, such as the airlines and banks, are what's behind this rally," said Michael Clark, head of equity trading at Credit Suisse First Boston.

He said investors are still reluctant to invest in small and mid-cap companies because they seek positions they can easily get in or out of.

This unease may reflect continued concern over the outlook for the economy. Despite the Fed's decision to keep rates steady, some economists say the economic problems overseas that hurt earnings at some U.S. companies will continue. "The global slowdown is almost certain to deepen in coming months and persist well into 1999," said Bruce Steinberg, chief economist at Merrill Lynch & Co.

Banks are amply demonstrating the current trend of big companies' getting sold last and bought again first.

For example, shares of Chase Manhattan Corp., which had tumbled 17% from their July 6 peak, gained 4% Tuesday, closing at $69.1875.

But smaller banks whose stocks have been weak for a much longer time are failing to snap back so well.

For example Mercantile Bancorp., St. Louis, bottomed out Aug. 13 at $47.50, a 21% fall from its $60 peak reached Jan. 2. The stock has started to slowly recover, rising 0.9% Tuesday, to close at $48.5625.

Eric Rothmann, bank analyst at Stephens Inc., Little Rock, Ark., said Mercantile's difficulties have less to do with global markets and more to do with problems at home. Specifically, the company's acquisitions of Mark Twain Bancshares and Roosevelt Financial Group, both of which closed last year, have failed to add to earnings as quickly as investors hoped.

He added that shares of Mercantile rose quickly late last year on anticipation the bank would sell. But the bank remains independent, and as the days go by investors are starting to conclude that "there are fewer and fewer deals that can get done in time for year 2000," Mr. Rothmann said.

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